{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How the PCA algorithm works"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA makes several assumptions that are important to keep in mind. These include:\n",
    "- high variance implies a high signal-to-noise ratio\n",
    "- the data is standardized so that the variance is comparable across features\n",
    "- linear transformations capture the relevant aspects of the data, and\n",
    "- higher-order statistics beyond the first and second moment do not matter, which implies that the data has a normal distribution\n",
    "\n",
    "The emphasis on the first and second moments align with standard risk/return metrics, but the normality assumption may conflict with the characteristics of market data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm finds vectors to create a hyperplane of target dimensionality that minimizes the reconstruction error, measured as the sum of the squared distances of the data points to the plane. As illustrated above, this goal corresponds to finding a sequence of vectors that align with directions of maximum retained variance given the other components while ensuring all principal component are mutually orthogonal.\n",
    "\n",
    "In practice, the algorithm solves the problem either by computing the eigenvectors of the covariance matrix or using the singular value decomposition. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:12.132258Z",
     "start_time": "2018-12-27T18:11:11.977772Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy.linalg import inv, eig, svd\n",
    "from numpy.random import uniform, randn, seed\n",
    "from itertools import repeat\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "pd.options.display.float_format = '{:,.2f}'.format\n",
    "seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:12.869584Z",
     "start_time": "2018-12-27T18:11:12.863882Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def format3D(axis, labels=('x', 'y', 'z'), limits=None):\n",
    "    \"\"\"3D plot helper function to set labels, pane color, and axis limits\"\"\"\n",
    "    axis.set_xlabel('\\n${}$'.format(labels[0]), linespacing=3)\n",
    "    axis.set_ylabel('\\n${}$'.format(labels[1]), linespacing=3)\n",
    "    axis.set_zlabel('\\n${}$'.format(labels[2]), linespacing=3)\n",
    "    transparent = (1.0, 1.0, 1.0, 0.0)\n",
    "    axis.w_xaxis.set_pane_color(transparent)\n",
    "    axis.w_yaxis.set_pane_color(transparent)\n",
    "    axis.w_zaxis.set_pane_color(transparent)\n",
    "    if limits:\n",
    "        axis.set_xlim(limits[0])\n",
    "        axis.set_ylim(limits[1])\n",
    "        axis.set_zlim(limits[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Create a noisy 3D Ellipse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We illustrate the computation using a randomly generated three-dimensional ellipse with 100 data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.284098Z",
     "start_time": "2018-12-27T18:11:18.237311Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_points, noise = 100, 0.1\n",
    "angles = uniform(low=-np.pi, high=np.pi, size=n_points)\n",
    "x = 2 * np.cos(angles) + noise * randn(n_points)\n",
    "y = np.sin(angles) + noise * randn(n_points)\n",
    "\n",
    "theta = np.pi/4 # 45 degree rotation\n",
    "rotation_matrix = np.array([[np.cos(theta), -np.sin(theta)], \n",
    "                            [np.sin(theta), np.cos(theta)]])\n",
    "\n",
    "rotated = np.column_stack((x, y)).dot(rotation_matrix)\n",
    "x, y = rotated[:, 0], rotated[:, 1]\n",
    "\n",
    "z = .2 * x  + .2 * y + noise * randn(n_points)\n",
    "data = np.vstack((x, y, z)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.288802Z",
     "start_time": "2018-12-27T18:11:18.285408Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot the result "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.542849Z",
     "start_time": "2018-12-27T18:11:18.290046Z"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mYxl2lLx5A/gcZganE1zYvfo5YykZUQBFNbaACIJAVsl9lqLe/pk9wSjPdAaJpLIc3+njvr0BI13hdDppaGi4rVTu5s2bCIJgWIr4rYT9fE/ZLIpMx9N5Xo3VcSdaQJPJxF/+5V/y0EMPoSgKv/mbv8nBgwf5wz/8Q06ePMkjjzyS33nWs+Dtwvw8YDgc5sqVK2uuaimUgLoCdqGJ/OUsoEUScVhMpLIKNnNuTbG0TK0vvxui0mtH0aCmxMbNcY1kVkHTVGJpmXq/E7/rzSDL0HSCf+wY5586gtgtIpIo0hOMMR5O8vHzDbede36p3P79+8lkMnTfuMF4cJJwy6s4BZmZaBafy4YgCCSzCg/uK1/ztVkOei3oZmOthdgPP/wwDz/88IK//fEf//GS79U07f6l/n5XElC3gIu1WtaCtSbzNU2jq6vLkCN8+eWX17psYHkCiqLA23aX8bOOCcOamCWRk/WlxNMy4WQWr92M07r0T1bptXG20c+LXWNUuiQiySzlHhsHd3h47z1vPiiuDs/xzVcG6A/F6JuKowFlTguiKBBpy/L+o9UoqsYPWkZoG55jp9/BR07tpOFWcl3TNF64Ocu3X5kjnNA4tauKzz3k5kvP9hCai6FoGsd2OHlgpxVZljekVE7TtDuSgBuBu5KAmqYxMTFBSUnJAq2WtWAtBMxkMrS0tFBaWrrmqKqqakzF05hEkVKnZcUoaGPAxUdP7WRwOo5ZEqkvc3JzMsqLPVOggQZc2FXG8bql91an6kupcUK7K8G9p45jMYsLCqQ1TePpq2OUOsx0KyqCAFZJJCWrVHltjIdTjM4l+euLfQSjaXx2M11jEf7zP3TwXz54D+VuG20jYb7xUj8OSSDgNNEdjDKXzPLDT9/P8FwSmwRSNqcB83Jvj9Fwu54JTXeqBdwI3HUEjMfjXLt2DYvFwvHjxwtOMeRLQN3F3bdvH5WVlWv6jLlEhqdbx5iNZ9A0qC9z8u6DKxcrlzotlN7Kpc3EM7zQHaLCY8MkiciqysWeEDv9DspcS+ftnFYTfoeE03b7T6uoGrOJDDUlNqwmEU0DQYCMrJDIKDgtEn2TMQanE3jtZkRBwO+yMh5O8VrvNI8creaFGyGsJhGrpJHNCpS7bUyEk4zMJQ0rCU6jw13vf+zt7SUcDhuCTOXl5Xlrb96Je8CNwl1FQD3ftnfvXiYmJtaV38uHgCMjI/T29hbk4gI82xUknpaNwMrAdJzLw3OrJuKziko8LTM2lwTAdMuKmUQRAZiMpG8jYDiRZS6ZwaQsX6RukkT2VLgYnE7Q4HcwHs5FTe0mCZdFwu+ycvHmFEMzCexmCdBoDLjQ0EjLuWtllgRU7VYg6ZY11wDTMqVpNpttwYRfvaG2paUFWZYN/Re/37/sfnyrlLGLBFwGelVLNBrl/PnzxiDK9WAlAuoTjxKJBOfPny+oUj6VVRidTVLlffMp73dauBGMUr/CcTcno7zQHSKj5AIosZRM9bxAjAY4rQtvxpdvTvFq7zQIGulUhjprhhPLnP+DJ2r56sVepmSFMreVZFqmocyFwypxpLaE1/qmcVgkBEHAJArcnIxRW+rgZH0pAO/YX8FLPVNEZQWzoDERSbG3wm30Da6ExQ21siwzNTVFMBiks7MTq9VquKvzS+W2qvlXl9zfStzxBJxf1aLn21RVLViTRcdyBEyn07S0tFBWVpb3xKOlYJZErGaJrKJhMeXOkcwqlLttkMkViAMLLGs4keWZzkn8TjNWs0QyI/NizzS9kzFKnGaSGYWaEvuCm308nOTlm1PsKLEjiQLRGFwZnuE9sfSCyKeOgNvKH7x7H8OzSXSnLpqWqS118HctI3jtFs41+rkyPEcsLZPMyNjNEs91BfmlAxXsqXDzuYf28o3nrzMTz/DgoXI+fKq2oOtkMpmorKw0XPtEIrGgVK6kpITy8nJkWS5awO3AclUta+2GWApLEVCXn9+/f7+h8lwoJFHg3iY/z3QGsVskFFVD1eBMYyltr6V54dVm7DYropI2GmxnFNst1w4GpuJEUllK7Gb2V7lxWE1UeWzsrnAbLinAZCSFKAhGElx3BSejSxMw9x5x3n7tTdT47LQMzlLjs/PAvnJaBmcYmUnidZhoGwlzZWiOx96zj2M7fXzuvh0oimIUI28EHA4H9fX11NfXo2ma0S4Uj8d58cUXjb1joXITq2GrNUHhDiXgalUthQ5XWekcw8PD9PX1FbzfWwqHa0oocVjoDkaxSCL7Kt0M9d3k5VGZqoZGJE2kptTG7oCJ6ekpOgaD9AVVros2JIsNl93CZDTNXCLLe+/ZgSQKBCMpOkcjpBWFPRVuXFYT6uI9pYbRp7cWnGvy80rvFCOzSWRVZWQ2yd4qN2UuG1lFJRRN8cKNSR49W7/pEoGCIBjzC8fHxzl37hyhUIiRkRHa2tpwOBxGZ8dGjdsuWkAWSjgsV9Wylnak5aATUFVVOjo6SKVSBac0VkJtqYPaUodRrdM2IyKLZmpKczfNyGySMncJpw8eZM++/Yw928WlvikcqTmCk1l8LjuzYQvjc3EkSeIfWsdxWiVMosAznUFO1ZdS53cwOJ3AZpaYi6Wo8Zjy2pMthttm5vPv3sfVoTl6JqMk0jJ1pQ4u9c8wMB0nJau0jYQ5VuvDsQUanfNhNpsNuQld7n5yctIYtz1fpqPQ7va3PAHzrWrZiB9e73x+9dVXKS8v59ChQ5t2Q8XjcZqbm6mrb0RNZfBY5ozXSl0Wbk7GOd3gxyyJPHigmrgsgAA+u5lSi8pQcIbXXr/ESFxAtLkoDfiwW+3YzBLto3N86EQt/VNxQrE0bsmJOicjrqGLYj4cFhPnd5VxptHPjWCMK8Oz9E7GARCBSDLL7z5xhT97qCq3n90GzJe718el6TIdPT09iKK4QFUu39/1LU3A9VS1FIJ0Os3g4CBHjx41clabAX0fe/ToUbzeEuxjg4Tmec/prIrH/uYTu87vpK7USanTgsUk5gIv1Tbee6yGpy4PEg5HGBsbI5VK4XQ6yZgcqEoVB6tzsheRSISbkdtvuIlwitf7p5lLZNlT4eZ4XcmKMhWSKPBv7mviV//XKygamEQBp1XCYZGYSWS4OpbgoX13hrCRLmevd7fr05n6+/uZm5vD7XYb7upKxdZvSQLqWi2qqm6KC7gUBgcHmZiYoLGxcV3kW20f1N/fz8jICOfOnTOSzqfqfbR1aczEM6iaRlZReXB/uZEb9DrMXNhdxuv902QTKjazxAN7y7FbJA7WlvJqWqOxqhxVVWkbCBGfifHEP75Mnc9KfXUFTqfztjzjVCzNd14bwCSJ2M0Sz3dPMh5O8i+O16z4/Wp8dprKndyYiOGymRAFkFUNURDIyLnqlNf7pvnKC71MRtM8sLecT97XiNu2PQJHOhZPZ4pGo0xOThpivn6/n/Ly8tuGib7lCBiPx2lpadkwrZbVoKoq7e3tyLJMU1PTusiu9wQuteb5n3P+/PkFIfT9VV7OVZko9TswiwJNARdD0wl+2j6OKArcU+PlaI2PGp+dlKxiN0tGhHN/pYdwIkv3RJT+qTjhpMahnVUoGgxoKtWYGBwcZHZ2litXrlBRUUEgEKB9ZA5BEIzkvcMi0TMZZSaeMapuloIgCHzkZC1//KMukhkFsySQyqoE3FYOVzq4PpnkD//pBqBhEkV+0DJMdzDKV//liTtGal8QBDweDx6PxxBjmp6eZnJy0hgmWl5ejtlsJh6P503A1QSZvvSlL/G1r33NUK3753/+5zpN0wYXn2drRs4sgxs3bnD48GHq6+s3/QdLpVK88soruFwujh8/jslkWlckdTldmEwmw2uvvYbT6eT48eNL5q/8dpEH9pZzYXeAwekEV4bn8LuseO1mXu+boWM8jEkScVlNCzriTZLIhd0B3n+0moDHxoP7yqn02Kj02tBEkZjJw8GDB6moqKCuro5wOMyrr77K5bYOwrPTJJNJ4NZDQxPIKqt///cfreYP3r0Xj82ErGg0ljn5z+87gEmA//PGBFlZwWExYTHl1ts5FqF/Kl7wdV2MjZbvkCTJ2PPfd999HD9+HKvVyl/8xV/Q3d3NJz/5SX784x+veA5dkOmnP/0pnZ2dfO9736Ozs3PBe44dO0ZzczNtbW188IMfBPgvS51rWy3gsWPH1nV8vqHwmZkZWltbF+QTdXXsQrGULkwkEuHy5ct55xFVVaNzPEyVNyc9ISEQcFvpGI1wuHqFigwBrCZhQaDFahIJJ7LgNy8I4e/fv5/AyAzfeqmHsYkgciaNLFrxed14LPnN9/vIqZ18+GQtaVnFahL57htD/M3FMSZiMqmsiqqB71ahuSDkCg42CpvdCWG329m5cydf/vKXefHFF/nsZz/L9PT0isfkI8j0wAMPGP999uxZgCX9/W3fAxYKXZZitQqJgYEBhoaGOHPmzAL3Yr25xMUWUNcBPXHixBoVu/XuiBwZ9ALplVBiN2M3m4jfUiJTNY1YSqGhyYmm3f6d9teU8oEzu3ipZwpZVXFKKifKNJovvWHMU6ioqFixW0EQBGxmif6pON97Ywi3VUQULfTPpIimcsrYipYrJt9XubIuzlqwVZ0QkPuOx48fX/V9+QgyzcfXv/51gJ8u9dpdTUBFUZYloKIotLe3G8Gdxe/bCALqujD63Ie1qq+JosDhGi/NAzOUe6yoWi5g8sDelQNDJknkoYOV/OzaOJFUCk2Dg9UeGgIuYtHIksecbvBztNZHRlFx3qr1hFzEUO9WiEQihlJaeXn5kt+leyKKpoEkQKnTTFYTGJ5NEk0r7K1082f/4vCahKRWw1YO58wXqwkyzcd3vvMdmpubAf7rUq/ftQRcKRmfTCZpbm6murqahoaGJS/Oegmou7AdHR2YzWbOnj2LKIrMJTKMzCawmCR2ljqM7vblcHynD7Mk0jEaRhIF7t8bMOTfV0Kl18avn61jNpHBZpbw5BF5tJhELKaFN7PVal0g7KsrpelPdJ2Mej6t3GNFAFQtFw3Vv+Pv3L+L995TteF7+a3qhFgLVhNk0vHss8/yxS9+kRdeeIHy8vIlNTruWgIup4w2PT1NW1sbhw8fNvJCS2G9BFRVlebmZqN2EeBmMMqP2seNoSYeu4kPnaxdkRySKHC0toSjtSXE0jI3JqI81xWk2menKeC+jTDzYZbEJZPhhZJgsVJaJpPTEdXzaV6vF39ZgH0VTi4PpLApWQQp17L0SwcrNiWQtlWdEGsJ9qwmyAQ5TdBPfvKT/OxnP1sx1XXXEnCxBdQ0jf7+fkZHR/NSRVsPAWdnZ5mdneXw4cPGXkBRNZ67PonPabnVSwcT4SSXB2e5fxWXEnLtSz+7Nk46q+KwmHhjYJax2RQP7i/ftpC+xWJZkE8Lh8MEg0EerowTyGSZwcLxpkp++UT9mmdP5IutsoCpVCpvRbR8BJl+//d/n1gsxoc+9CEAWltbn9Y07TalpruWgPM7IvRkPnBb3m05FErA4eFh+vv78fv9C4auJDIyyayyQBnaYzcbTbXzoWoaI7MJ5hIZfE4rVR4bQ9MJUhmVilv9gy6bidFwkpl4Ztmuhq2E3stnc7q5nnTRl7pBvd9KhRDm9ZdfxOPxGO5qvp3u+eBO7YZfTZDp2WefXXzIkjJpdzUBVVU19nu1tbVrSuYXIsrU2dlJPB7n/PnzxqQlHQ6LCafFRCIjG0K64UT2Nm1MVdW4NqXQd20Cs5STDWwKOCl1WG+r3xSATB65us3C8EyCy0OzmESBk/WllLut/Kf/e43LQ7MomQzdsyqXJ+189V/eiyinCAaDtLS0oCjKhrUO3YmaoBuJu5aAoigyMzNDW1sbR44cobS0dM3H50tAvZPB6/Vy6tQpBEG4LQ8oiQLvOljB01fHmEtkQdModVm5p7aErvEIvaEYLquJcreN8ZjK27w2RDEXSe0LxalospFVVWRFxSSJJDIyJklYsVJlM3FlaJavvtiHSC418rNrE/zykR20Ds/hd1iIk8VqtTAbz/JM1yQfPlmL1+tlz549ZLNZQqEQw8PDtLW14XK5KC8vp6KiYs3W8U61gBuFu5KA+rDFZDLJuXPnCnpy5UtAfcjmrl27FgxdWaoSps7v5DcuNDA2lyQ89sqeAAAgAElEQVQrq4zOJfmvP7tOJJXl4A4vdovE6/3TpOcFbwVBAEHAYpI421BKy+AsigZ2k8iD+yo2bW+1EjRN4wfNI5TY3pRBnI1n+EnbOLnl5iy1bq8Xu9mLW4ei0ahhHWVZNqxjPjMoigS8wyDLMq2trWSzWXbv3l2w25APAUOhENeuXePYsWO3aYUsNyPQZTXRFHDxd5dHmI1lcmO7LBI3glHONPpxWc10Z9RbN5aEqmoIaJQ4zJS5rDSUuUjJCk6LaUPzaWtBVtGYSaSp9r55bZ1WE1O31K6TWYVQXCY+F0MURWpW6D2cX4u5e/fu22ZQOJ1OKioqlu1UKBLwDkIikcj11dXVUVJSsq46wZUIqEdUx8bGFnQyzMdKY6qnYmnCiSw+lxlBALvVRCaRZTKSotRppcwuMTwdQ5Gz2BwOjtT6jELppXJ1Ww2LSaQp4GJ0NmmsayaR4USdj/cdruLfPXGVrCF1r/JHT1/jRH3pkjIXizF/BsXiToVsNktZWRkVFRWGdSwS8A6BPihE3+/pI7UKxXIEVFXVaI86d+7cshHV1caMaYDdLOGymoilZUBAUTUiqSzHygRc8hgWl5dMLAShGYbE2IZHENeDXz9Tx5ef7WEsnHMvA24rHzhWwz9cHUVeNGcikVH5xkv9/MmvHFrTZyzuVNBV0uZPaLJarRs+HXcpFAm4DDRNo7e3l2AwuMAaiaK46hTTlbAUAdPpNM3NzVRWVtLY2LhiRHWlMdV+pwVJhN5QnD0VLq6NRggnM0iig532LGo0zX3n347b7V6wR2pubkZVVSNgsZZu7o1GpcfG7zzQRCiaxmM301jmxCSJ/Kg9tw/k1lfXABUYnF5/B8R8lTRN04jFYnR3dxvtQ/Ot40bnBosEXAKyLHP16lUsFgvnzp1b4IpIkkQqteTU37ywmIC6HMaBAwfyatJdth1JVnmhe5KsrDIRTnF9PMKJuhJ+c3c9qelRUvEo2RKvMZF28R5Jrz7p6+sjHA7j8/mMvr58tE42on2nNxTjz37SRSia2/M9fLiKXW/LVf47LSa0WzL5xhQm2NBhLJC7Lm632xDtra2tZXp6mvHxca5du2aIMlVUVGwIcYoEXARdR6WhoYGdO3fe9no+Y6pXwnwXUp94tJZOhuVc0JuT0ZxMe8BFQ8BFMqOQzMjMjdzA5XBw+vRpXn311WWJsrj6ZHZ2lmAwyM2bN5EkiYqKCioqKnC5XJtiHWVF5Y//oZNoKovfZUVRc/MkmsqcjEdS3JyMIoo5d1r/9OoSO//yXP2GrwUwCu5NJpPx3SEXnZ6cnKS1tZV0Oo3f76eiomJFhe2VkEgktkQKZTHuSALq+72loo86NkIZTdM0uru7mZmZKaCTYek95OhsckHtpyrLtF/v4dDZBg7ubQLynxO/uK8vmUwaKtLJZHLZm249xByYzlXo6NU3kihgs0j87xf7GJ1NYjWJlNhNzCWy2C05uYw/euTgpkVsVVVd0vLPF2XSu9z1a2Oz2QzrmK9kYTKZ3FRtoOVwRxFQb+0JhUKcP3/ecNOWwnotoCzLJJNJstksZ86cWXOkbTkSlbosjIWTJLMKXcPT9I8Fcbi8DKft7Moo2G+1AhXiKtrtdqP4e/5N19HRgcPhoKKiYt3VHDmd0Te7HSBnFUdnE3jsOaGogFnCIshIJhP//aPHNjVdkk8tqN7lrhNIlyxsb28nlUoZGjBlZWXLnust74LO1wNdvN9bCutRx04mk1y6dAmTycShQ2uL3OlYzgLW+hx8+9VBbozPMhNN4nM7OVXrJxTL8Fr/NA/s3Zji6vk3nR6wCAaDXL9+nUQigdVqpaKiAp/Pt6bPq/TaONNQyiu907htJtJyrhvBaTMvaBQWEVC1hc3Em4FCuiHmT/edrwHT1dVlzJ/QraN+7rc0AfVqk8bGxgWdxiuhUBdUl6c4cuSIUcBdCBZbsVRWIRRN80b/NFYliZ0s+2vLsEgSwWiavVVuBqbiZHflSLuRWid6wMLtdlNWVkZfXx9er5fBwUGuXr2K1+s1kt35uNmfe2gvT7eO8WJPiIDLykdO7eSfOif43utDiFYBAUjKGg8fDCyQye8JRvmH1jGsZon3H91BTZ7TfVfCershFlvHRCJheA2JRMJQRotGoxsmyJROp/nYxz5GS0sLfr+f73//+0bL2mJsOwF1KYdjx44t6C5YDYW4oENDQwwMDNwmT1EI5lvA0dkEP+8OISsqP73cj8Os0bCjAhWwmSVm4mmSGQWLSUQShIJd0LWsbX4p2NzcHMFgkL6+PkRRNIIZ8ycQzYfNLPHhk7V8+OSbD8P6MgfxtMyP2nL9jscrzPz+u/YYr/+0fZzf+0ErWVlFEAX+6vmbfOs3z3BimWGi+WKjE/EOh8OwjqqqMj09zQ9/+EN+/OMf09rayqOPPsrv/M7vLHu8Lsj0zDPPUFNTw6lTp3jkkUcW6MF8/etfx+fzcfPmTZ544gn+4A/+gO9///tLnm9bSy40TTP2e2shH6zNAmqaxrVr1wgGg5w/f35DXA09DaGoGi/dnMZuEogGh9nhtYDVhd0qkcoqhBNZBGA6luFobQmiuPkEXLxOn8/Hvn37ePvb387JkyexWq10d3fz/PPP09raysTExKrX0mqSeOw9+/n55+7nqU/fS1OJyPebR+gaj6CqGl946hrprJLLC6oayYzCHz3dse71b2YljK6g/alPfYrz58/z53/+58taKh3zBZksFoshyDQfTz31FB//+McB+OAHP8hzzz2HsIwfva0WUBAEDh8+XNCx+e4Bs9ksLS0t+Hy+JceNFTpkRCdRLC0TiSeJTg5TVVlJRa2HZ7uCzMQzVHhsDM0kqCmxU+GxEnBZFxy7HZg/MFO3APre0WazGdZxuYdUKJrmY994nalwCrGnn2+8PMBv39fEXCKLqoGYU9VHgA2RJ9zKUrTGxsYFBfdLIR9BpvnvMZlMeL1epqen/cDU4vNtuwtaKPJxQWOxGM3NzcvOmlhJXHc16Mem4xGGBwc4sLsenzenBnayzofDIuG2mShzWyhzWknLGv/YMcH9e8q3lYDzoVsAXaoxHo8TDAaN3Jqulja/a+GrF/uYS2SxSgJ2u4msovLf/rEbyE3KVVQNPSh6YMf61dHutFrQfASZlvltl/zjXUvA1VxQPZd4/PjxZd3b9RT7CoLA3NwcY2NjfPD+Y7SMxMhEUiiKRiKrgABto2GqS+z4nBZEQSCZUbg8PEvtHaIavRhOp5PGxkYaGxuRZdkYB9be3o7b7aaiooJro3OYJRFZyTULK2pOXn9fpYeuiSjcGlntsJj4k/cXFmGejzuNgPkIMunvqampQZZlwuEwwMxS57trCbic1dI0jb6+PiYmJlbNJa7U0bASNE1jfHyccDjMfffdh9lsptrvYSKcom8qRjCSosRhJpVVuD4RwWYSaSp3YzWLufIuy8YrPm80TCbTgq6FSCRCMBikXErQFs2QVUG4JYkoiQI7SuyUu61MRtNEUzKfe2hPXupuq2GrCJhOp/OKEOcjyPTII4/wzW9+k3PnzvHDH/6QBx98kCeffHLJH/zOElxcJxRF4erVq0SjUc6dO7ci+aCwSKqiKFy5coWZeBrBVUZGzT0I/C4rB6u9TITT7PDZcVhM7CixY5FEeiZz46inY2nq/I5NdUE347yCIBjd7g8c34d8qxZUvfX/sqqRSCQxm0R2lNgpcZoJJ+RbuqWFF8zD1uqC5rMVmS/ItH//fj784Q8bgkxPP/00AJ/4xCeYnp5m165dfOlLX+Lxxx9f/nwbtvptRiqVorm5mR07diyrBboYa7WAmUyGN954gxHFQ9+cnUQiRmein6M1JdgsIhZJJJaWcdwifm2pg1hKZiKSYjyc6607XufjRufoHW8Bl8MrvdNYTbdcd0nCJAhkFYWBmQS2uRhZFWbT8OVnuxHE3DX5X4+e4HDN2qLcOrZSGTtfrCbIZLPZ+MEPfpDXuX4hCBgOh7l8+TIHDx5cUz3fWixgNBqlpaUFT1Uj40NJKj0KUdLIisb/eaWfB/aWY5ZEYpks8SmZxoATURDwOSy8bXeAM42leO3mW/MTNjcIs5ktTAG3FVEQEEUwm3KBKLtk4nPvOYDXbuGrL9xkdiyMpiqoikw0I/Af/+4KT//btxdEpM2eDbHduOsJqHcynDp1as3V7PlawFAoZAR0OkIZrKYMoqghqyrD03Gskogkvjn+azqeZjqaAeBUg49zTWWY51WM3CmjuwrBr5/Zyd+1jBBLKgiiioDArkoX7z9ajSAI/Me/b8dptdxSeNNQFIXB6STP/vPzlHhcRpoj38bjO9ECbiTuWgJqmkYqlWJwcJB77723oLng+VjAwcFBhoaGOHv2LDabDV88QlZRyWgqnZMpxlMyqqZROWmn1GnBZTXhtpl496Gq3GcsUah8p6QhCkGd38l3//VZ/r/vv0xcdHHfngC/fd+bzcs7/Q56J2PYRAkQUDSRCq+Fdz74dqNeVZcuzKfxeCss4HaS/K4koCzLXL58GUEQOHXqVMGDNleygLoOaCKRWCD22xBwUu6x8fOOUWYSCmazBY9NYiaeoS8Ux2UzcazWt2KHgCAIhEIhbty4QSAQoLKyclt60QrF3ko3/+aIjfvvv3Dba59/aC+f+e5lklkZTcvJ5//Be/YhiuJt4kzzZe9LSkqMetVCHqbrQTKZ3JZCbLgLCagLM9XX15PNZtfVkrScBdQJ7na7OXny5IKns9Uk8b4jVbQNhrBrEpWVfibCSRRFpXM8wq8er1kx/K7XZiqKwokTJ5ienqajo4NkMmmQcb1ittuJk/WlfP+T5/hR2ziyovKew1Xsqbj9epjNZqqrq6murl7QeNzb27ug8XgrPIXtEuWFu4yA+uAVXZhpbGxsw6fc6q1K9fX1S3biAzjMuRRDx1yYvqk4wq2StGM7fTywgjSDpmm0t7eTyWQ4cOCA0VRaV1dnCBLpYrYej4fKysptsQjrRZ3fyacf2JX3+5dqPNbbh2KxGG1tbVRUVKzYz7cebFcrEtxFBBwcHGRwcHDB4JX19ATqx88n4NzcHFeuXOGee+7B7/cve5woCuzw2vjJXJam6lzlo12TiKayDE7H8Tktt01EkmWZlpYWw9VabOEWCxLpHQy9vb2GHENlZWXeHd6bjamkyr9/4gqXh+ao8zv4D7+0h2M719f5oMNut1NXV0ddXR0///nPqaysJBgM0tXVhd1uN6zjRlmtIgFXgKqqdHR0kE6nOX/+/IL93nplKeZbwPHxcbq7u/OOpjosEo0+E167BUkUcJea6BgP88PmEbwOM3sr3ZxvKkMSBdLpNG+88QZ1dXXs3LmTrq6uFV2r+WPC9u3bRzKZZGJigra2NjKZzAJXdSsiqtOxnDjT2FyK57sncVolvnopRUYIYTVJdI5F+NR3LvP9T56lzr+xDwhBEBb08+mBHF1HdH69aqHXokjAZZDJZGhpaaG0tJRDhw7ddoHXK0uhW9CbN28yOTmZty5MVlEpcViwSQL31HiJpWWuDs1hEkVqSx04rBKd4xGqS+wEbBotLS0L1NbWGgW12+1GD5teozk4OEhra+uC4EWhwajlMBvP8MnvtHB1aA5FyxVZOywSmgaxlEa5R0ISBewWiURG5h9ax/jMg7s3dA2LobvtTU1NxgyKoaEhWltb19x4rKNIwCWgJ7737t1LVVXVku9ZrwsKOdfW5XIZE25XQlpW+Pn1SVpHwmQyWSbjMj9pHyealJmMpThSU4LDIiEKAm6riY6BCVyxYU6cOIHH82ZnwHrSEItrNGdnZ5mYmKCnpweLxYLH40GW5RXPMR1L86c/7uLFnhAVHhuff/c+7tsTuO19n/+7Nq4Mzhoq2Ao52UWHxYQGRFNZYxybpuUk6zcSq12jxTMo9PmFr7/+umE5Kyoq8Hg8K1rHIgEXQff3jx8/vuDGXYz1uKDZbJbBwUHcbjdHjhzJy325eCPE5aFZdnjtyIqJV7tVKhy5+ezuaRPprMLwbII6v5NgaIa0Oss7f2np4TEbEd2bH7yA3I3U29vL1NQUFy9eNFzV+Xk2TdP4tb9+jYGpOIqqMRPP8KnvtPCd3zqzYJSapmn8c9ckyqJ1JrMqPmfuQZWWVTRNQ1Y1zJLIew4t/aAsFGvJAerzC0tKSti7dy/pdJpgMMiNGzeIxWKUlpYagZzFnkKRgLewWAV7M4qp4U3N0bKysmVlGRZDVTWuDs9R5bUhiQKpjIYggEkSObDDi9Us0ROMcn0iQnRuhkwyzm+8b2nybVYi3uFwUF1djaqqHDhwgFAoRF9fH5FIBJ/PR2VlJWMpM2NzqZyup5DTd0lnVf7PS/0c/38WBlEsJvE2qyYIIAoCdgnsNjOprIrLauL33rWXQ9WF1Xsuh/UUYlut1gWNxzMzM0bjsS5YpQszFQlIrhqhtbUVSZLyUkWDwiygnso4duwY0WiUdDqd13GCkKtqUVVAhJSsEk4pKDMJnuuaYC6RJZqSiUainNzv5Fceuhe3fel9yFZUwix2z2ZmZpiYmOD16xOoirJAyExDuzW/YuEaf/Peer7x8sACEtrNEllFxe8Q+eG/vYD91mDSzZAm3KhOCFEUKSsro6ysDMhZPD2o1dPTw5NPPmnMNcw35TMzM8NHPvIRBgYGqK+v58knn8TnW/gAu3r1Kp/61KeIRCJ0dna2AV/UNG2BOMwdke1NpVK88sor+Hw+jhw5kvdFX+secHh4mI6ODs6ePUtJScmaLKggCJxt9DMeTjEbT9M1HkESBEQBro9HmU1kEDIJvA4zGUfFsuSDHDmGh4cZHx9fdb+2ERAEAb/fz8GDB/nE+x/AajGhqjmrrqoaVkngvftLb3so/N679vLZX9rNzlIHO7w23n2okt9+WwN/8sgB/uheJxUeOx6bedN0QTerRMzhcNDY2Mi5c+f4wAc+QH19Pa2trZw9e5Zk8vaR4kvh8ccf5x3veAc9PT284x3vWLLlyOFw8K1vfYuOjg6AdwP/XRCEBUrT224Bs9ksr776KocOHTKkEfJFvgTSNI3r168TiUQWpDLW2o50tsGPzSTyk2vjOULukAhhR9USpJIJDtWUsKu6jJ7JGJFU9rZcoI66ujo8Ho+R+rDb7VRWVhY0QXatsJhEvv2JM3z6u5cJhlOIgsBHjvqpk2Z5/vnnKS0tpbKy0kh6//bbm0hmFL756iDNAzNcGpjhTL2Pj+zc/PTHVtSBut1uqquruf/++/ngBz+Y93FPPfUUzz//PAAf//jHuf/++/nzP//zBe/Zs+dN1ThN08YEQZgEAsCc/vdtJ6DZbObChQsFVXvkMyFJb6C12+2cPn16wX5vrXtIURQ4XleK02qmeWCayaE5sorIjJokUOahsqzEGFoirbCvXBw8icViTExM0NzcjKZpRtI93/3pWnGo2svzn7ufqVgGt82EzZyrLtH3ShMTE3R1deFwOEhbSvjmKwNIkoB4y3V+rW+GPTYz9234yhZiq4qkC9kDBoNBIzpfVVXF5OTkiu8XBOE0YAF65/992wkIFFxqJUnSins4vUm3pqZmSbm5QiUpqn12WgYFYmkZmzIDVhcmswVJEBiZTXKyvtQY7ZwPXC4Xu3btYteuXUb0Tle4Lisro7KyMq9xzvO/Vz7vCbgXBrnm75V0te3vvnwDWZbRFBAlEUmUyCoa3TMbm3JYCtutB/POd76TiYmJ2/7+xS9+cU3nHx8fB/g28HFN0xbccHcEAQvFSnvASCRiNOku59oWGkV1WU0cLtXoV2T27trHXtHEZDSFrGi8c38F9+1dmys9H/Ojd4qiLBhY6fF4qKqqyntU2Xqgq22fPtDIXzfPIACappKVZVBVyiyqMbNvs0iy3QR89tlnlz2moqKC8fFxqqqqGB8fX7YRPBKJ8N73vhfgP2ma9tri1+9qAi4XBdXziKuNGyvEAmqaxs2bN4lNTXG+zskDF/IvOl4rFncFzM3NLUi667WjG13JPxvP8GTzMH1TcS7s8nOyrpRLAzNkFDBLEjUlDi7szKmad3R04HK5jD3sRk6z3W4CrgRdeOmxxx7jm9/8Ju9///tve08mk+EDH/gAH/vYx7h8+fKSGhV3NQGXsmDzZ7tvdB5RVVXa29vRNI0zZ85w8eLFgtZdCObXh+7fv594PM7ExASXL19GURQjydzV1UVjY2PBnzMdS/O+v3yJcCJLVlH5Sfs4b99dxp/+yiEuDcywu8LNO3eX0Heji3vuuceY8DsxMWFUoOh72PXOMFzvXIh8UQgBH3vsMT784Q/z9a9/nZ07dxoaMM3NzXzlK1/ha1/7Gk8++SQXL15kenqaz372s1dvHfqvNE3T//vuJuB8C6jLz2cyGc6ePZvXD7cWC6h3M/h8Pnbv3m3cWHo1icMirWnft144nU6amppoamoik8kwMjLC66+/jslkYmpqCrPZjN/vX7MF+c5rg4QTucCWWRJRFJWLPVP8u3fs4T2Hc0GHeDxunHf+hN89e/aQTqeNII6+h9VnGK51LXeyBfT7/Tz33HO3/f3kyZN87WtfA+DRRx/l0Ucf1V86utR57moC6nvA+fLzSxVtr3R8PgRMpVJGj+B8WfKZlMrXXuwzktgn6ny8fXfglh7K1iGbzTI0NMTp06cpLS1lamrKGOXsdrsN9zCffeONYAxZUY2pR4IgIAkCg9Nxo9F4JTVxq9VqtBLpe9ixsbEFa8m3WPpOJuBG4a4nYCaT4ZVXXmHXrl2r6vovRj4WUC8KXxzMmY2neXFEZt9u2FFiR1Fz4fkdXht7KtcvyZ4vdEW4+dOE588NjEQijI+P09fXt6DnUL/hOsci/OFT1+gaj1Dnd3Jhlx+zSTLm8qmaRkZRkVWNqViaMpc1bzn/xXvYSCTCxMQEr732GpIkGQ+G5dq/tpKAxY74AhCNRpmZmeHcuXNGTm0tWM0CTk1Nce3atQVF4bG0zI9ax7g2GqYtJGP1xakvczA0kyAYTvHTdoH6MhcW0+bfONPT07S3ty/bw6gL6nq93gV9ha2trWQyGRwlfv71/x0lkVGQRIGboRjDM3H2VXq4EYwiCJDIqIDG//v37WQUlc88sItHT6x9yOj8tezdu9cYt71YjmN+X99WEVCW5W1THbhrCajLEXo8noLIBytbwJGREfr6+gw1NB3/1DHBwHScmlI7NhP0h2J0jkUocZhJywrXxiL83yujfPhUfoNGC8XExATd3d2cOXMm76f3/L7CbDbLty5eJyMrCGg5iXlBIKtqvH1PGf/x4X28fHOar7zQi6KqJLMyiqrx5ed62FVqIrDOAoH547aXk+PIZrN3rTZOvrjrCKjPkZ+enubs2bNcunSp4HMtZQH188/MzNzWgZ9VVK5PRNlRYkMUBPw2kclklkgqS4nDjN1s4khNCdcnIkxGU5S7N6esbGhoiKGhIc6dO1dw2N9sNuPxliBJYyBoaFruf4qqMTI6SvkeO2gqsqKiAVklVycqqyr/4e+v88f3l3Jsg77PUnIcExMTDA8PYzKZ0DRtgdv8i4S7ioCqqnL16lVMJhNnzpxBEIQNk6TQz9/W1oYgCJw+ffq2p68oCFhNIrKiYTEJ7Kt0M9MfxoSJgFOiodyDw2JiNpklnS28U38l9Pb2EgqFOHv27Lo74N+xv4I//XEXaVVFEkBDwGaR+PW37SeZjBCdHEFEIzXvEgvkIr/fbovwLx5Y33dZCvPTLfrDRRAEw23eajmOzcZdQ8BMJsOlS5eoqqpaV55rPub/gLIs09zcjN/vZ9euXUv+uJIocGFXGf/YGcTnMOP0Bdij2onGkzjkGKNDMwgWB3aHk3L3yjnItULTNLq6ukgmk0s+HApBqdPCN/7VSR77u3YGpxOUe6z80fsOcKShEqjk39c18qPB5xkPv1nuJwhgFlTGYpsvF6goCk6nk+rqakOOY3JyckvkOLYKd8Wq9Ujk/v37qaio2PDzp1Ip3njjDRobG6mpqVnxvacbSnHbTFwZnsMkCrzvyA5G55JcvBFCUVUkJcOpgMLLL76Az+czSsfWk1DWNI3W1lZEUeT48eMb+uQ/UVfKM//hPrKKiunW+GwdTquJpz9zgXf9xUWiqSwWScQiqMiaQLlV5urVq1RWVq77+y2Hxd0QJpNpQY/jYjmOQiqDstnstpL3jifg/LkMK8lTFApFUXjttdc4dOiQ0bC5EgRB4MAOLwd2vNn93RhwcbKulERGpsSRU0nTm2DHx8e51tFJd9RMT8xMmdfFe49U5y3hpygKly9fNhLdm+V2zZ9dMR8Bt43/+evH+XffvUwqm0Uym3GYJf7Lr5+k3CIzMTHB9evXjZaqysrKVSuQ8sVK3RCLO0r0yiBdLU1Pf6wkew/bmwOEO5yAi+cybDRCoRCJRIL7779/xZrRfGC3SNgtb1oBvQnW7/dzNTbAyzdHsQppxqfDXOoZ5bfP1/DgkcYVn9bZbNZwuxsaGta1vvWgwZHlP52xEHXuwm6z8I595YYYk66fqpej6UGx+S1VhWItaYj5lUG67P1iOY6lLHWRgEtgubkMG4nh4WEGBgZwOp3rJt986F3l+lM3lVV4vjvEzjI3kigwHUvTNjLHnz43SktvkAvVJmp2VFJVVbVgHbqWaGNj45oLDDYSo6Oj9Pf3894HVh6A43a7cbvd7N6922ip6uzsXDbHlw8KzQPOl71XVdVwVXVLrT8cbDZbkYCLsdJchuWQb2WG/t4bN24wNzfHuXPneOmll9a8xqlYmu7xXKJ6X5WHUqcFRdV46WaI1/tm0DQ4VV/K2/aUkb01R10UoGs8QttIGFXTMEkCz46aUVw+PtFoM27W8vJyfD4f169fX/O8w5Wgqhqjc0lKHGbcy3TqL8bQ0BDDw8OcOXNmTYnqxS1VoVDIyPF5vV6jHG21vddGJOJFUTQ8EXiz+bmlpYVsNssTTzyBqqpruofy0TsZk+IAACAASURBVIPREYlE2L9/P2NjY3+padpnFr9+RxEwmUzS3NxsKEjnAz2Xl4+VnJ9mOHXqVEE/bl8oxvfeGELIpa954UaIR8/WMTgd5+fXQ+wosSEAF3tCDM7EMUsiFpNI13iUzrEwGhqiICAgEE5keLl3hs88uIczO3ciyzJDQ0NcuXIFs9msN3Kuu+eubWSOf//EVWYTGTQNPnq6ls8/tG/FmtX+/n4mJiY4c+bMuoIUesmZnuPTrdGNGzew2WxGOdpSrvhmdEPMb36Ox+M899xz/PznP+fo0aP87d/+LYcOHVr1HLoezGOPPcbjjz/O448/fpschY4vfOEL3HfffXzve99b8vU7hoD5zmVYDFEU8/qh9ILtpdIMa3n6/VNHELfNZFiRuUSG564HmY1nqfRajWDGVCzNT6+NU+uzoygafdNxFA3QcpNlrSaRrKKQlVUSGRmwEo1GGRwc5MKFC7hcLqanp42eO70Zd60h94ys8m++3UIkJWOWBBDgiTeGObDDyyNHdix5jK4tevr06Q0lwPzAyYEDB5ZsqdJdcVVViUajmxqhdDqdPPjggyQSiRXnuC9GPnowAC0tLQSDQd797nff2QSMxWJcvXq1oCm3ekfESi6SPvGoqanptv1UvgSGHFFDsTTVJW8GhNw2M8FwGqtZRBcVS2UVWofncJglKjw2BEFgMpZGADKKhlnKWU9FA7/LQq3PweTkJJ2dnZw5c8bYkwQCAQKBgKH6PD4+Tk9PD1arlaqqKiPi2DkW4XuXhoinZd5/tHqBynX76BxpWTVqU3NrUHn66uiSBOzu7iYSiXDq1Cm6JqJ885UBpuMZ3nu4ivcfrd5QBbTFLVXBYJDu7m5isRiyLBv7tM2Evgdci4udjx6Mqqr83u/9Ht/+9reXbFvScUcQ0Ol0cuHChYKedqtpg+rSFIcPH17Ssq7FhRUEgcYyJ2NzScpuJdqnYml2l7up9tn52bUJKjxWZhNZMopKlddhWNZKj42B6Tg+q4nZRBZF1fDYTfy3Dx1hfHyMvr6+ZZuI56s+79+/39jHXLp0ia5pmb+8kspZVwR+fn2Szzy4i09cyBUruG1m1EWBIU3TSGQUvv3qACfrS9lf5TES/alUihMnTtA+GuET37xERlYRBLg8OMu10TB/+L6Dq16nQmCxWKitrWXHjh1cunQJh8OBqqq88MILmzqqbbnhnOvVg/mrv/orHn744QXta0vhjiCgIAgFuxor6cLoOcSVpCnWKkvx4P5y/vpiHzeCURwWCZ/TyoP7yvHaczfGa33TmESBgMuK61aDbi4yKvz/7Z17WJR12se/z5w4DAhyHAZURFEQT6AcxJa0NA0lNQXUNitf62239art2tra2i73rXTbXd+3dlOrrVZtTcECLTPWbc08Eah4AI8c5DQHBgYYmBMz8zy/9w98HgcEnYEZZqD5XFfXlV7yPPcw853f7/nd9/29sTZ1LOrUBsg1ekyTBuJXD0xER7McdQoF0tLSbP5wWT/HvLfjFCyMAQKKAARgaArbv6/Cz1PHwUvIR2yYH+IjRqFCpgHQXetptDC4ItfgirwDfB6Fp+ZGY15YF2iaRmJiIiiKwo5j1TBZmNuOaYTgwHkZNj4Qy6UgHA1N0zh79izCwsK4aid29VcqlaiqqoJQKLyjpWowOMsPpri4GCdOnMD27duh1WoBYB1FUVpCyCvW/84tBDgY+mspYtMM98oh2mNLoeow4vMf62GhCfg8CqN9RXgibRz8b4kvLSYYaTHdq2xGbCje/c8N6Ew0CCGYJPHDL+ZNhK/otihv3LgBjUaD1NTUAT9rKTu7IBKwztQENE2jy2RB0dEfECMNRUREBHY8logdP9Tg6DUVaIZA1WGEl4DP9ft99EMVEjIlmJcyk1slFRpDj+0mj6IAHtCqNzlFgAzD4OzZswgNDe1Rami9+sfFxXGu1hcuXOAS7hKJBAEBAQMqUnCWH8yePXu4/9+5cyeeeuqp3b3FB4wAAfbegvZOM9xrZfXx8cGlS5cQGRl5165xg8mC/zl0BXKNAd4CPryFfIj4PFxsbMd9sXe6oKVNCMYHEbNwVdGJUT4CxElGcR/oTqMZe4+Wod1gwdI5Uwd1wjl3Qgi+KVcAoGBhCCw0wZggMZYuuA9qtRoymQytra14KDwAT8ychLeOyqHWmrgPq8VihoBHgRcY2eMDvCA+HJ+cvMkdUJksDEaLRYh28Pw/oFt8Z86cQUhIyD3rfFlX65iYGC7hXl1djY6ODgQFBSEiIsKuU2O9Xm93eaMtfjC2Qt1jRoHzK24HyeXLlxEWFobQ0FAwDMPNl5g2bZrNOcTOzk7I5XI0NTVxBxwRERE9Wn3+dVmB949WYWxQ97elzmQBj6KQERuKJ+eOv+Oaap0J5Y0aAEDi2EAE+nZfq6XTiGc+OYFOEyDy7m5reix1LFan2JZ26U2LtgvZHxSjTq0DId3F0mH+3vjnhhRMDLttIdHW1gaFQoHPSmX45qYF3kI+aJrpPpXhCfD1xvsQGXg7FaA3WbDx8/O40NAOHq+7C2Tb2iTMGBPYTyQDg135goODMWHChEFdhz01bmlpsdmp7a233kJCQgJWrFgx4HvbSJ8fxmG/Alr7wrBbmAkTJti8HbE2FYqLi4NWq4VCoUBJSQn4fD4nxiqVFv7eAs4vRSwSQKYxws+756+w5KYan564iTO1rRAJ+Agf5QV/byE2PTIF0UE+2PZ1MTrNFMaGddeSWmgGe8/UY/FUCSdSewgWi+At4MHfWwAhrzvnaDTTeK2wArHhfug0WJA1Q4oH48MQFBSEV8fH4sKHpyFr1cHCAEI+haw4fwT1OvvxFQnwyZPJqGnWQmMwI0Ea4PAuf0eJD+jeCVmfGnd2dkKhUPSwv+hrxHdzc7PDalcHwrAXII/Hg9FoRHFxcZ9pBnvx8/NDbGwsYmNjYTAYIJfLce7cObQrjPCFEBoDA5GADwtDwKeAORNun6xWqbT4+PhNVDV3QiTggQLQpjdB7CXAh8eqsEyqQyvtjUC/2xsLAZ8HHig0dXQNSIAGMw1lhxFikcDqS4fCmdpWXFN2gAKFk1UtWH/feDw3fyLEIh5emS1CtTEQtMgfUyPEkAj0OH/+PCwWS49cHEVRiAm1Ly1kKwzDcNOPByu+3lh/qVrbX5SXl6OrqwuhoaHw8fGBSCTCV199hQULFjj0/vYw7AVoNptRW1uLWbNm2ZXAtwUfHx8uTxUV2473v7sKS5sWOj0NgcgLT6RGIzLw9gP8jzVqCPgUdF00fIQ8UBQFg5kGBQYXapR48Wczke5lxmfFdfD3FnDPVhTVbXc/oBiFfAT7eUGjN0Mk6BZgh9HcPcNP2P320gzBzlO1eDwlCuUXziFm3BjM61VpFBMTw+XiWFv80NDuQxxHN7+y4gsMDMTEic4zNmbpbX+hUqmwdetW7N69G2lpaQgIcOxcQ3sY1gJUqVRobGxEdHS0w8XXm3FhgfjtI0m4UN+ODkMXwoRdEBpUOHasjls1+Lzu4/oAHyG0RjO8hHwQQtDUosGUMcGIiIjAkiALTlerUduiA3PrgGPZDCmqVVpMkY7qty2oPyiKwuuZ8Xj5y0vQ33ouBcClQACARwFmhsEPxaVIjOu/55HNxY0ZM4ar4ayrq8OFCxd6HHAMpjqGYRiUlZUhMDAQsbHOnSffFwKBAP7+/igpKcGnn36KwMBAdHZ2DnkcLMP2EKa+vh51dXWQSrurORy9jbEV9htVLpejpkmDgloKQpEXbjQboDVawNA0xgT74s/ZidwBhoVmcLGxHbUteuwtrUPbLSPc0b4i/G/OTIwN9oXJwqBNb0KQWGSTKOvUOvz7ShO8BDxckXfg2wolvATdq7DRbIG/gEHeUzO435c9EEK4A47m5ma7vUZZWPGxvY2uQK/XIysrC88++yyys7OH8tZ9biGGnQAJIbh+/To0Gg1mzZqFpqYm6PV6l3yb9oamaZy+XIv9ZxtQJtNBawbCA7wRFiBGVJAvXlsypcfK9FphOU5VtXDPfhqDCfGSUVieGIl3v7sBg5mGr0iAlxdNxv2Tbe+KaNeb8PTuc7jZ0m2ySzE03l0Zh/unD97Kw9prtKmpCSKRiCuLu1u+lRCCsrIy+Pn5YfLkyYOOYyCwsxqys7Px5JNPDvXth78AWVMmoVDIOWArFApoNBrExcW5OjyOS1X1eOPgZUSHj4apywiD0Qh1Fx+5s6Kw+r5J3BZu4f8eAwDwKB68hd2rXHNnF0QCHryFfHjdOtE00wR7nk5FRIDtz4kX6tvwiz1l0BuM8BIJMTUqEO+tTrS5FclW2IJqpVIJhmEgkXT3NlrX9LqD+CwWC9asWYOMjAxs3LjRFSEM7zQE2x0eHh7eY7s50BFjzqK+vh7l128iOCgYo/x90cYXoUZN0Gk04YNT9WiQNeLB2ED4BYWhXW9Gh7H7uU3ApxAqFoEmBFqjGb63uuu9hXwYLWaU3mzFspm2nfDSDMHLX1xAu9YIM6Ggpy0ovdmKT07U4IWFjhWAdUE1OxeCNdsNCwuDRCLBzZs3IRaLXSY+hmHw9NNPIzEx0VXi65dh4XpqMBhw+vRpREdH3/GsZ++ceGdSVVUFuVyOhzNSwOfzoO+icb6+HTRhIBIIMDY0ABd1/qD9I7CntBGgzSAMA4YwMJgsqG/Tw0Iz0BgtuNmiQ6vOBKD7EIUtYbMpDrkadWo9upjuQyGa6S6+3l8mc9ZLB3B7LkRqairuu+8+BAQE4Ny5c1CpVDCZTFCpVEP+ZUkIwQsvvACJRILf/e53Q3pvW3D7FZCdfTBjxow+HbDZdiJX0pdl4ONzxuH9o1XQm2h4CXgI8RMhPMAbLZ1duKo2o1rLx8SIIBhMZjRp9NAaLTBYgKhRAlSZGVgYBqrOLjCEINTfG+kTbDvl7ejoQOWVi2BtSW/bvBO03xL0UMDn86FSqRAVFYVJkyZxBlWD6W0cCK+//jpomsbmzZudep+B4tYCZHvk7tYn6OoVkLUM5PP5SEpKglpngsFEI31CCHxFfPzP11cgCfCGn5eAK34O8BEizN8L9Wo9Any9EODrhepmLSzaLgh5FMb4Ac16QGchSJD4YdPy6TaNPmObmuemJkN04tQtc+BbrUgAt611NuzvxMvLC3Fxcd3jsK2qVNrb26FQKHDjxg2nuKmx/PGPf0RjYyP+8Y9/uK2Jr9sKsK6uDg0NDfcctMnj8WCxWIYwstvQNI1z584hICAA42Im4MPjNThX1wqAQrBYhOfmT0Ti2NG43tQBiqKg77LAS8DHfbEhiAjwxlvfXIVa1wUeKBCGQZBYBLFYDLFYjGCahqpdh0VSE6ounYFWIoFUKu33i6i1tRWXLl1CSkoKxGIxlkyLQFGFkvOjEfB5WJF0d89TR8CKTyQSIT4+/o4PvrXz9ZQpU7jSv9LSUvB4vH5Lxuxl27ZtOHv2LPbt2+fW8yXc7hSUEIJr166hs7MTs2bNumfSl/XN1Ol0kNz6kLJlVM6kt2VgUYUCeWcaMGa0DyiKQqvOhEBfEX67eDKKLitRVteOqCAfzJscioPn5ThV3YI2nQkBPkIkRwdhQXw4dhXXQtFuACgKhADzJofi5cVxMJlMUCqVUCgUMBqNXOJ/1KhRoCiKm+JkPail02jG6wcqcPxGMyiKwuKpEryxdArX3+cMWPEJhUJMmTLF7vfAaDRyr9NkMt3xOm1l165dyMvLQ2FhoUvrPHvh/mkIhmFw/vx5iEQiuwZtAt3HzE1NTZDL5dDpdAgPD4dUKrX7zbOFviwD3zx0Be06E1ecTQiBQtOFLSunIcTv9ofg7W+u4OhVFZo6u7hhKBGB3vj86TSM8hbi2HUVGtsMmBYVgNTxwXdYQLAtOOzrFIvF6OjoQHp6ep/GRgYTDYqCU4XHvt5Lly5BIBAMSHy9MZvNaGpqglKpRGdnJ2dtGBwcfNdrf/nll9i2bRsOHTrkbsNc3FuA/aUZBkJvMYaFhUEqlQ64adMavV6P0tJSTJkypUcn9Lbvq3BZpkHoLasKC82gRWfC/+XO5E4wdV0WrPu0BJUqLXigwON1PxNaaAaPz4nGbxfbl8uUyWS4evUqAgICoNVqERwcDKlUes8PqaNhxcfn85GQkODwe7OTdhUKBdra2hAYGNin5X9RURHefPNNfPvtt05xUR8k7p0H1Gg0iI6OHlCpVG8EAgFnzMqWilVVVUGr1SI0NBRSqfSeluV90dHRgXPnzvV5Ips5LQKXGtuh6uyCgEdB29XdBmSdPuDzKNAMAWEAnoD1Z+m2hb+m7LArFplMhpqaGmRkZEAkEoFhGLS0tEAmk+HSpUtc7WZoaKhTn4EIISgvL3ea+IA7J+2yvY1Xr16FWCyGWq2GxWJxZ/H1i9usgEMBTdPc9q2jo4NbGW0RY2trKy5evIjZs2f36y/T0KrH0WsqtBtMmBMTjNnjgu7w3vzgWDX+erQSfB4FHkVx5kzZs8bg1wttq49kDXNTUlL6rMVk51LI5XK0tLQ47difEIKKigoAsPuRwVH37+zsxB/+8Ad89tlniIuLw8svv4ylS5cOaRw24t5b0KGmtxjZlbGv1hs2HZKSkjLo5wozzeCdoqvIO9MIECDAR4gxQT54b02iTQM9a2troVAokJycbJOYrI/9VSoVfH19IZVK7S6k7uu6FRUVIITY7D7gDCoqKvD444/jwIED4PF40Gg0Npnr2kJDQwPWrVsHpVIJHo+HZ555Bs8///xAL+cRYH+wrTdyuRwajQYhISGIjIzE6NGju7scamqQkpLi0BM1pcaIc3VtEHvxkTo+uMdgl/5gDXNnz549oJYg605xpVJ5h7+oPde5fPkyGIZxqfgqKyuRnZ2N/Px8p3RXKBQKKBQKJCUlcafyBw4cwJQpUwZyOY8AbYFhGE6MKpUKFEVhxowZCAsLc2kyl3VQmzVrlsOe6XQ6HeRyOfcNz9pv3G1iEys+mqYxffp0l/1OGhoa8Mgjj2Dnzp2YMWPGkNxz2bJl+NWvfoWFCxcO5Mc9ArQVa2e1sWPHoqmpCW1tbU49ZaQZAnm7AaPFoh4tS2xeVK/XIzEx0WkHKgaDgfvGZxiGE6N1QpydWmWxWFwqvqamJixZsgTvv/8+0tLShuSetbW1yMjIQEVFxUAPeTwCtAX22YamacyYMcOqlrL7lFEul6OtrQ1BQUGcGAcrivJGDd48dBkagwUUBeQmj8GT6dEAul3fLBZLj1icDdvVIJfLYTKZuOqUhoaGIY+lN62trcjMzMSWLVswf74ThtT3gVarxf3334/XXnsNjz766EAv4xHgvWALAXx8fPoso7L+d2q1GnK5HK2trQPyo2QxmGis/qgYNEMg9hLAwjDoMFjwh0cSINbJwOPxXHLCyGI2m6FUKnH9+nWYzWaMGzfOYTlVe+ns7ERmZiZeeeUVLFmyZEjuaTabsXTpUixatAgvvvjiYC7lEeDdsFgsOHv2LEJCQuwyCmLtGuRyOdRqNUaPHg2pVGqzGMvq2/C7gnLO2h7odlKLDyT479Swu34RDAXsFthoNGLq1Klobm6GQqFAR0cHQkJCIJVK7R68ORAMBgOysrLwzDPPICcnx6n3YiGE4IknnkBQUBDefffdwV7OvQVYUlKCgoIC5ObmcvMJhgqTyYTS0lJuqORA6S3GwMBASKXSuybDbzR1YuPnZQjwEXKvWd6iwcJJgXgje2ieb+6G9fOn9XvCVqewW/Lg4OAB7wLuhclkwsqVK7FixQqsX7/eode+GydPnsTPfvYzTJs2jXtNmzdvRmZm5kAu594CNBqNKCoqQl5eHq5du4bMzEzk5uY6/ZjbYDCgtLQUkydPhkQicdh1eyfDAwICEBkZeYcYCSF4ft8FXJZr4Cvio71DBy+RAP/4r3SMCXJtLWN/4usNwzDca1Wr1QgICOAS/4OdL0jTNNauXYv09PTB5ODcAfcWoDV6vR6HDx9GXl4eampqsHTpUuTm5g40/9IvWq0WZ8+e7Xd0maNgy6fkcjmam5sREBDArYx8Ph/aLgv2ldTh27JqRIf44xcPTcPEMOcY4toKO6cvKSnJri9A61IxlUoFPz8/SKXSAY0WY60kxo8fj9dff93el+BuDB8BWqPVanHo0CHk5eWhoaEBy5YtQ05OzqD9Rdjm1aSkpCE1Zu0txlGjRiE8PBy1tbUYM2YMxo0bN2Sx9MdAxdcbawc1pVIJHx8fLvF/t3kN7M++8MIL8PLywjvvvOO2DbV2MDwFaE1HRwe++uor5OfnQ6lUYvny5cjNzbW7e4Ltn0tOTh504+dgIISgpaUFZWVl3PhmtkzM0bPRbcVR4usL6yocgUDA5Rr7sjP8/e9/j5aWFmzfvn0kiA8YCQK0pr29HQcPHkReXh7a2tqwYsUK5OTkIDo6+q4/x1ohpKamOn388b0wmUz48ccfERsbC4lEAo1Gw1XgWG/dnO2bwnLjxg10dHQgKSnJ6V3ker2eS/wD4FZGsViMP/3pTygvL8euXbvcupvdTkaWAK1Rq9U4cOAA8vPzodPp8OijjyI7O/uO8cD19fWor69HSkrKPbdAzsZoNKKkpARxcXF3zKdjt24ymQwqlQpisZhbGZ0lxsrKSmg0miERX2/YTviDBw9i27ZtEAqFyM/PR0KCc8Zhu4iRK0BrmpubUVBQgP3798NkMmHVqlVYtWoVjhw5gsmTJ9vcReBMDAYDSkpKkJCQgNDQO4d7WsOKkZ1fyHYzSCQSh72OyspKtLe3O7TOdCD885//xK5du7B69Wr85z//we7dux36Xq1fvx6HDh1CWFgY10Y1hPw0BGiNUqnEF198ga1bt8LPz49L4to7EdWR6HQ6nDlzBtOnT+/TZvFuWA8TZQ817jXZ915UVVWhra3N5eIrLCzEX//6Vxw6dMhpz+XHjx+Hn58f1q1b5zYCHDEb7L6QSCSIjo7GsmXLcPjwYRBCkJ2djQULFuDDDz9ES0vLkMaj1WpRWlqKmTNn2i0+4Pbcu7i4OMybNw/x8fHQ6XQ4ffo0SkpK0NDQALPZbPP1qqur0dra6nLxHTlyBH/+859x4MABpx6KZWRkDOj37kxG9AoIdK8aAHqcpNXX1+OLL75AQUEBxGIxcnJysGLFCqe+OaydhbPSHtYro5eXF6RSKSIiIvpdGaurq6FWqzF79myXiu/kyZN48cUXcfjwYYSEhDj9frW1tVi6dKnbrIAjXoD3ora2Fvn5+SgsLMTo0aORm5uLZcuWITDQcbPQ2Zzj3ewsHIlWq+XEyE4vsp55X1NTg+bmZiQnJ7tUfOfOncPTTz+NQ4cOOcQLyBY8AnRjqqqqkJ+fj4MHDyI8PBy5ubnIysoalMkPa5jrqpwj23SrUCggFAohFAphNpuRmprqUvFdvnwZjz32GAoLCzF+/Pghu69HgMOEa9euIT8/H1999RXGjh2LnJwcZGVl2SWivgxzXcn169chk8kgEAggEAi4bepQm9dWV1dj5cqV2Ldv35CPlXM3AYIQcrf/PBBCKioqyBtvvEGSkpJIdnY22b9/P9HpdHf9maamJnLs2DFiMBiGKMq7U1NTQ4qLi4nFYiGEEKLT6UhlZSU5fvw4OXXqFKmpqSFGo9HpcTQ0NJCZM2eS8+fPO/1evVm9ejWRSCREIBCQyMhI8vHHHw/l7fvUmGcFtANyywMzLy8Phw8fRnx8PHJycrB48eIeVTVKpZKrtnEHa/Ta2loolUokJyf3WeJmMBi4bSpFUdzK6OhKIZVKhczMTPztb3/DnDlzHHrtYYBnC+pICCE4f/488vLyUFRUhOnTpyM3NxdNTU0YPXo0li5d6vJqG6B7yI1cLkdKSopN9aW9xWiLUZMttLW14eGHH8bbb7+NBx98cFDXGqZ4BOgsCCE4c+YMNm3ahAsXLmDhwoVYs2YNHnzwwUF5bw4We8XXG2ujJkIIIiIiIJVK7RajVqtFZmYmXnrpJWRlZdkdxwjBI0BnotFo8Oyzz+Kjjz5CeXk58vPzcfToUaSmpiInJwfz588f0hK4wYqvN0ajEQqFAnK5HAzDQCqV2iRGo9GIRx55BOvXr8fq1asHHccwxiPAoYZhGJw6dQp5eXk4fvw40tPTkZubi4yMDKe2G9XX16OxsRGpqalOuU9XVxcnRpqmuZWxt2u42WzGqlWrkJWVhQ0bNjg8jmGGR4CuhKZpHD9+HHl5eTh9+jQyMjKQm5uLuXPnOjQfx4ovJSVlSFbc3mKUSCQIDw+HWCzGz3/+c6SkpODXv/610+MYBngE6C5YLBZ8//33yM/PR0lJCR544AHk5OQgLS1tUGJsaGhAfX09UlNTXdLxYTKZoFAosGPHDuTl5WHixInYsWOHXS5zIxiPAN0Rs9mM7777Dvn5+SgrK8PChQuRk5OD5ORkuzrBXS0+FkIIXnzxRZjNZsyaNQsXL150hKXfHRQVFeH5558HTdPYsGEDXnnlFYffw8F4BOjudHV14ciRI8jPz0d5eTkWL16MnJyce7qSNTY2oq6uzuXiA4BNmzZBoVDggw8+cJqVBE3TmDRpEv79738jKioKycnJ2Lt3r8NNuxyMR4DDCVttGmUyGWpra91CfFu3bkVZWRl2797t1EOm4uJibNq0Cf/6178AAFu2bAEAvPrqq067pwNw7wm5Hnri7e2N5cuXY/ny5ZxN45tvvtnDprG8vBxBQUGYN2+ey8X30Ucf4cSJE9i/f7/TDaVkMlkPu5GoqCiUlJQ49Z7OYsQ15O7fvx8JCQng8Xg4e/asq8NxCL6+vli1ahX279+PH374AfHx8Xjqqafwm9/8BidOnEBNTY1L49uzZw++/PJL7Nu3b0gKD/ratQ1X57QRJ8CpU6eioKAAGRkZrg7FKfj5+WH+/Pnw9/dHcXExJk+ejJdeegkpKSnYvHkzqqurhzSegwcP4u9//zsKCgqGzGUuKioKDQ0N3J8bGxuHGuc2hgAAA5VJREFUrJ/Q4fRXpU2GeTfE/fffT86cOePqMJwGwzA9/tzW1kZ27txJHn74YZKWlkbeeecdcvPmTafGcOTIETJnzhzS1tbm1Pv0xmw2k/Hjx5OamhrS1dVFpk+fTioqKoY0hgHQp8Y8AhyBqNVq8vHHH5OHHnqIpKenk61bt5L6+nqH3uPkyZNk9uzZRKVSOfS6tvLNN9+Q2NhYEhMTQ9566y2XxGAnI6cdacGCBVAqlXf8/dtvv41ly5YBAObNm4e//OUvmD179lCH51b0Z9M4mC1bWVkZNmzYgK+//hqRkZEOjHZE89NKQ3gEeCdKpZITIwBkZ2dj5cqVdtk0XrlyBWvXrkVBQQFiYmKcFepI5KdnS+ihJxKJBL/85S/x/fffY8+ePbBYLHbZNNbU1GDt2rXYu3evR3wOYsStgIWFhdi4cSOam5sRGBiImTNncglbD31ji02jTCZDVlYWPvnkEyQmJrow2mHLT2sL6mFg9GXTOHfuXKxZswbvvfce0tPTXR3icMVjyuQovv32WzJp0iQyYcIEsmXLFleH4zQqKyvJ5s2bSXh4OMnPz3d1OMOdkXMK6kqGaSHwoCCEDNtKEzfCcwjjCEpLSzFx4kTExMRAJBJh9erVOHjwoKvDcipDIb6RWEJoCx4B2klfhcAymcyFEY0MRnoJYX94uiHspK8tu2d7Nnji4+NdHYJL8KyAdjKiCoE9uBzPCmgnycnJqKysxM2bNxEZGYl9+/bh888/d3VYwwJbSgh/angEaCcCgQDvv/8+Fi1aBJqmsX79+pE2y9xpfPfdd64Owe3wCHAAZGZmIjMz09VheBgBeJ4B3Zj169cjLCwMU6dOdXUoTqewsBBRUVEoLi7GkiVLsGjRIodev7y8HHPnzuX+XFZWhgceeMCh9xgInkS8G3P8+HH4+flh3bp1rphnN6Jg7fRlMhn4fD7mz5+PrVu3IikpaahC8JgyDTcyMjJQW1vr6jBGBDweDwkJCbh8+TIqKysxduzYoRRfv3gE6OEnQ1paGk6dOoXt27ejqKjI1eEA8AjQw0+ItLQ0PPnkk3juuefcppP/Xs+AHlwMRVHRAA4RQkb+SYyToSgqFsAPAGIJITpXxwN4TkE9/LR4HsCr7iI+wCNAt4aiqL0AigFMpiiqkaKo/3J1TMMRiqImUBR1DYAPIWSXq+OxxrMF9eDBhXhWQA8eXIhHgB48uBCPAD14cCH/D7NMMwBPllSSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.figure().gca(projection='3d')\n",
    "ax.set_aspect('equal')\n",
    "ax.scatter(x, y, z, s=25)\n",
    "format3D(ax)\n",
    "# plt.gcf().set_size_inches(12,12)\n",
    "# plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Principal Components using scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [sklearn.decomposition.PCA](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) implementation follows the standard API based on fit() and transform() methods that compute the desired number of principal components and project the data into the component space, respectively. The convenience method fit_transform() accomplishes this in a single step.\n",
    "\n",
    "PCA offers three different algorithms that can be specified using the svd_solver parameter: \n",
    "- full computes the exact SVD using the LAPACK solver provided by scipy, \n",
    "- arpack runs a truncated version suitable for computing less than the full number of components. \n",
    "- randomized uses a sampling-based algorithm that is more efficient when the data set has more than 500 observations and features, and the goal is to compute less than 80% of the components\n",
    "- auto also randomized where most efficient, otherwise, it uses the full SVD. \n",
    "\n",
    "Other key configuration parameters of the PCA object are:\n",
    "- n_components:  compute all principal components by passing None (the default), or limit the number to int. For svd_solver=full, there are two -additional options: a float in the interval [0, 1]  computes the number of components required to retain the corresponding share of the variance in the data, and the option mle estimates the number of dimensions using maximum likelihood.\n",
    "- whiten: if True, it standardizes the component vectors to unit variance that in some cases can be useful for use in a predictive model (default is False) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.548470Z",
     "start_time": "2018-12-27T18:11:18.544584Z"
    },
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.71409739,  0.66929454,  0.20520656],\n",
       "       [-0.70000234,  0.68597301,  0.1985894 ],\n",
       "       [ 0.00785136,  0.28545725, -0.95835928]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(data)\n",
    "C = pca.components_.T # columns = principal components\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First principal component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.557362Z",
     "start_time": "2018-12-27T18:11:18.549951Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.71409739, -0.70000234,  0.00785136])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explained Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.564568Z",
     "start_time": "2018-12-27T18:11:18.558773Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.92923132, 0.55811089, 0.00581353])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explained_variance = pca.explained_variance_\n",
    "explained_variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.580337Z",
     "start_time": "2018-12-27T18:11:18.565442Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(explained_variance/np.sum(explained_variance), \n",
    "            pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA to reduce dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:18.595348Z",
     "start_time": "2018-12-27T18:11:18.581405Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca2 = PCA(n_components=2)\n",
    "projected_data  = pca2.fit_transform(data)\n",
    "projected_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.762504Z",
     "start_time": "2018-12-27T18:11:36.596113Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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77iEtJ2+88Qb++te/Lsp+5nJFmELZtm0b+vr6MDQ0hKKiIrz88st48cUXyc+zs7MxNTXF/7OcYZj3ATxKxXL1Ep12jUQiAGKjSaHHmC+K5DgOLMuS40fDv1aiyJRyfll1gikSiRCJRMjCyrv2OJ1OQa49vNtPOntlLMuio6MDBQUFqK2tFfwFnk8w3377bXAch+LiYtjtdhw8eBAPPPCAoON+8MEHUKlU4DgOZWVl8Hq9KCgoQHt7e1zBnI1SqURZWRkxK7Db7WQcF8uyMXuf/Hs9ePAgfD4fDAYDOI7D8PAwenp6cNFFFwk65/lYjj3MVJBIJPj1r3+N66+/HpFIBA8++CBqa2vx+OOPY+vWrdi3b9/5PkXKIsGnXS0WC7Kzs5OmThMNchCyJiQ6Lr9G8GLKcRx8Ph+mp6dRXFwMhmGIkPJiygssFdPlYdUJplgsJndmfr8fLS0t0Ol02Llzp6AvjdAh0rNxOByYnJxEVVUVqqurU3rufOfldrvJPqRSqYTH4xF8XIlEQu5G+QjV6/Um7DM9ffo0Dh48CKVSidtvvx3FxcUx5xg9jisUCsFqtWJ0dBRTU1MIhULEZxb45C6Z47ikKWmhrDTBBIAbb7wRN954Y8z//eAHP4j7WI7jrliGU6IsIrPTrgMDA9i0aVPS2odEN8ALqVfg14no9YIXzXj7pdHQ/dLlYVUKJsuysNlsOHPmDGpra1MyIkhHME0mEwYHB1FQUJD2fl2ii2jr1q04ePAgFAoFvF4vrr32WsHHvO666/DCCy+gtLQUExMT0Ov12Lx5My655JKYx3V2duLQoUN44403oFQqwbIsOjs78dRTTyUUO6lUisLCQhQWFsLlcqGlpQUcxxGXJLPZDIZh8PnPf37R7PNYll3ywdKrZRwaZemYL+2ajl90NEtV4BdPTHn410u0XxotpmKxOCYqpWKaGqtOMBmGwdDQEBwOB3bu3Jly43wqgsmyLM6ePQu/34/du3ejr68vrYthvovo4osvRmZmJiYnJ5GXl0ea7c1mM4BzbRCJoq6SkhL8/d//PY4ePYorr7wScrl8zufR1taGn/70pxgfH8epU6egVquh1WoxPDyMgYEB1NfXo7GxEc888wxJO15xxRXk+SMjI3jsscfQ29uLXbt24fvf/z7ee+89nDp1Cj6fDxkZGTh27FiMdV+6F+FyRJh+v39RzRYoq4dE1a7R39dU1od4tRCLLZhC6i2SiWl08RHHcejr60NNTU3MfiktPhLGqhLMUCgEu90OjUaDhoaGtBZXoReE3+9Hc3MzDAYDNm7cSC4sIRdDJBLB5OQkGIYhfX/zPa+6upqkeSORCF555RV0d3cDADZu3Ijbbrst4XvNzMxEQUFBwkInfp9TpVJBJBIhHA5DoVBgenoaU1NTMJlM+M53vgOFQgGGYfDDH/4QhYWFqKmpAXAu/Tg1NYW8vDx0dXXh6aefxne/+92YKDYQCMBqtWJ4eJi0nfBmAamIk1Av2YVAfWQvPOardp2N0PXB4/EgGAxCpVIteVZkIcR7n263G2KxOKb4aLYw0+Kj+Kzc3/QseI9WlUqFysrKtBdWIReE3W7H6dOn56R7hZiv8247/f394DgO9fX12LNnj+C7zqGhIXR1daGiogIcx6GjowNbtmxBeXm5oOfPRqPRkCIdlUoFv9+PcDiMNWvWID8/H62trbDZbMjPz0dOTg5mZmYwODiImpoacByHkZERaLVaeDwe5OTkYHBwcM5rZGRkxAyDdrlcsFgsOH36NAKBAHQ6HQwGQ9JZlkLbPRYCFcwLg+jIym63w2w2o6amJun3a76ULMdxxNOZYRhIJBL4fD5EIhFIJBIolUrI5XIEg0FSU7AY3+elEqhUio9mR+EXqlnDqhDMaNeekZGRuOXYQkkmmEajEUajEdu3b58zjUPI/sbQ0BB6e3uJ4LW1tSWtIOU4DmazGZFIBIFAgFxk0T1fs7FYLJiYmEjagH/zzTejs7MTo6OjKC4uRlZWFnQ6HS677DJkZWXhD3/4A0ZHRzE5OQm9Xo+cnBzibsMwDHbu3In3338fYrEYbrcb11133byvF23dV1VVRbxcLRYLuru7Y0Z1ZWVlxVxgNMKkLBQ+7RoOh8m1yjAMgsFg2kWB4XAYY2NjGBsbg0ajwYYNG5CRkYFwOEy+r6FQCF6vF263G+FwGAMDA/D7/eA4DnK5HEqlMuaP0Bm8S7EfmuyYQvZLo4uP+EreoqKiT33x0YoWTN61JxwOE9cevugnXRIJJsuy5LUaGhriRkJCIky+oZl/PH/s+e5a33zzTbS2toJhGCJaw8PDAM6ZokdXswLA8PAwfv/734NlWQSDQVRWVhJrvNloNBp8//vfx9TUFJRKJWZmZsAwDIqKivDCCy9AKpXiiiuuQEtLC6xWK77+9a/HtKR885vfhEqlQktLC/bs2YP77rtv3vc/m9lerj6fD1arFf39/ZiZmUFWVhbp/VyOPUyv10v3MD+F8NEQv4hHp12jK+uTEb0+eL1ejIyMwGazobCwENu2bSN917OPJ5VKkZ2djczMTExMTKCurg7Auevb7/fD6/XC6/XCbDbD6/UiFApBJBLNEVKFQrGiepFnE09Mw+Ew/H4/uXbnM2uYLajzpcdXIitWMHnXnuLiYlRUVJAPlO/DTJd4gun3+9HU1ISCggJUVlYm/OUJ2cMsLy9Hbm4uhoeHwXEcSkpKUFxcjNHRURKp8QUyOTk5ZAxVSUkJGIbB8PAwbrjhBshkMjAMg6qqqjmmAEeOHIFSqYROp4PX60VjYyO+8IUvJBQbflg1gJgqX6lUCpZlUVZWhuLiYpw5cwYHDx7EwYMH8ZnPfAa33XYbVCoVvvCFL2BkZIQ4CC0EhUKB0tJSlJaWEus+i8WC5uZmzMzMIBgMguM4aLXaJVk4aIT56YFPu4ZCoYRFPABSvsl2Op0YGhpCMBhEWVmZoFRuIhiGgUKhgEKhgE6ni/lZJBIhQurxeGC1WuHz+cCyLGQyGfmeBgIB+P1+ZGRkLFhY0jVtmQ8+M5QsMuVvamaL6WraL12Rgsm79tTX10Or1cb8LJW7xXjMFszp6Wm0tbVh48aN0Ov1SZ+bTDAVCgUefPBBDAwMgGEYVFdXk/FSlZWVUKvVUKlUZLZlIBCA0+mESCTCwMAApqamUFtbi1tvvTXmuNFmDRKJhLwH3h0nnS/Wtddeiw8++AAjIyPw+XyYmZlBeXk5ZDIZ/vCHP6C8vBwXX3zxklxkQKx1X01NDZqbm6HRaDAxMYGzZ89CLpeTmwu1Wr0o5+Dz+ahgrnL4tKvVaoVGowGQeD8OELZmsCyLyclJmM1mqFQqrF27Nq0WslSqZMViMTIzM+cMh+A4juyDTk1NwefzoaenB4FAgAjw7MhUaOHRUlzLQhy6hDof8ecXCoUwNTWFwsJCIqISiSSm/ed8iOmKEkyO49Dd3Q2Hw4GGhoa4dmuLmZIdHh7GyMgIduzYIWgRFZKSBc4ZENTV1YHjOPT392NwcBDHjh0jw5nr6uqwZ88eAOcKjJqamvD6669DLpdDo9Ggo6MDDQ0NMBgMcDqdOHDgAMxmM0pKSrBnzx5cddVVePbZZzEyMoJQKIRLLrkkrS+PTqfDj3/8YwwMDGB8fBy///3voVarMT09DbPZjMbGxiUVzHjo9XoyuNrr9cJisaCrqwsejyehdV8q0Ahz9TI77drV1YXdu3cnfd58dQvBYBAmkwkTExMwGAzIz8+HTqdLu996Ma4ThmGQkZERs/7xVfQsy8Ln85HI1G63w+v1xhQeRf+ZXXi0FNse0Tfz6RBPTP1+P5xOJ4qKisjvPBgMxjyGF8433ngD+/btW5bresUIZiAQIGOy5nPtEYlEcfPjQuFbK06fPg2WZbF7927Bv2z+uUKIRCI4ffo0pFIp1Go1QqEQSUN2dnaioaEBGo0GWq0W9957L8LhMHJyciCXyzEyMoJ33nkH1dXVaGpqQjAYRElJCcbHx3H06FHs2bMHX/7yl2GxWJCRkYHR0dG0Pw+1Wo36+nqUlpbif/7nf3Dy5Em0t7cjEAigt7cXMzMzePDBB5dFMGffqSqVSpSXl6O8vBwsy8LhcMBisZBK3dzcXJLaFroIUMFcXfDRRzgcnpN2FfqdjHeT7XK5YDQaMTMzg5KSEuzatQtisRgDAwMLuiFfbOJVqPJtYrPhC4+8Xi+cTicmJibmFB5lZGQgEokgGAxCKpUuynW9UMGMRzgcJhFlsuKjn//859i7d++ivn4iVoRgpuLaIxaLifF3OkQiEfT09KCioiJmb1QIQiNMn8+HpqYmMjWlsbGR/Izfd4le4A0GA4qKisgeRVlZGW688UaIRCIcOHAADMPA6XRCKpUSn1e+EtXv9ycUTJfLhXA4LMhMICcnB48++ihuuukmsCxLvGJ/85vf4KqrrlqWQpn57n5FIhGx7lu3bh2x7jOZTDhz5gxUKhVJ38ZbTHioYK4OElW7prPA82lSjuMwNTWF4eFhiEQilJWVzfGETtc6cyXAFx7Njo6jC4/4OoGzZ88uWuHRUjh08YKZiOj90kAgsGzX9HkVTI7jMDg4iPHxccFp0YV8oW02G0ZGRlBSUpKWnZuQPUy+h/Oiiy4im/y1tbXIzMyEyWQCy7LYtWsXsrKyyHMyMzNxyy23oKmpCSzL4tprryV7M5dccgna2tqQmZmJ0dFRGAwGHD58mKQnE6WOjhw5gjfffJPY2d19991Jv9R8bybLslAqlfD7/WCYc+OK+N+NyWSC2WzG2rVrF20wN08q6aJo6z6O4+DxeGCxWNDe3g6/34+cnBwYDAbk5ubGTJTxer3zCirl/BKv2nWhKUQ+nXf8+HFkZ2dj/fr1CS0hV7NgJiK68EilUsHlcpFWNyGFR9F/4hUeRSKRRZlWFE0yweRZbqvL8yaYoVAIp0+fRkZGBnbv3i34okin6IfjOAwNDWFsbAwVFRVp738lizBNJhOGhobmiL9KpcI111yD9evXQyaTIS8vj1SHKpVKFBUVwWAwzDH5BoDLL78cSqUSExMTkEqlMJvNsNls2LZtG3JyctDR0QGn04mzZ88iLy8PWq0WNpsNhw4dQlFREcRiMU6fPo26urqk/aCZmZm488478dRTT2F6ehoMw2DTpk2oqKiAz+fD888/j8cff5wUK7z22msoKytL67OMR7r7KwzDQK1WQ61Wo7KyEizLYnp6GhaLBX19fRCJRNDr9dBoNHC73UmLu3gOHTqEL3/5y4hEIvj85z+Pxx57LObnP/vZz/Dss89CIpGgvb39MIAHOY4zpvwGLnD4tGswGITRaERZWZmgaJK/HhN9Z3w+H0ZGRjA1NQWO47B161bB04yS4fV6Y2bYLtWWxWLXD8z+vIQUHnm9XthsNphMpriFR0uRtUlVMJerxuK8CWZPT0/cHsNkpFr0E4lE0NbWBoZh0NDQgNHR0bSrbBNVwPH7kh6PJ2EPp0wmI4YAFosFL7/8MimHv+SSSxL2UUqlUjQ0NGBsbAx/+MMfyOd18uRJrF+/Hlu3bkVzczN0Oh3GxsbQ3t4Ot9uNmZkZFBQUQCKRQCKRwOv1CnqP3/zmN7F+/Xq88847KC8vxwMPPIBAIACHw4HHH38cMpkMUqkUU1NTePLJJ/Gf//mfQj++pCxWQYJIJEJubi5yc3MBfGLdd+DAAfzHf/wHysrK4PP58LnPfS7hhRaJRPDII4/g7bffRnFxMbZt24Z9+/Zhw4YN5DGbN29GU1MTlEolGIZ5BcC/A7h7wW/gAiFe2nViYgIVFRWCns/fPEd/ZziOg8PhgNFoRCAQQGlpKaqrq3HixAlBN8rz3RTzI/CGh4cRDoehVCoxNjZGRIQXkFAoRKYQrbSeSqECHF14NNt2c3bh0czMDFwuF4aHhwUVHgkhHA4LilqXO2N03gRz48aNaT0vlT7M6L1E/q5VLBanXTQULyUbCoXQ0tKC7OxsbNu2TdCXsaWlBSKRCCUlJYhEIjh+/Di2bt067zBqr9cLsVhMxFgkEpHKUZFIhPz8fOTn54PjOExPT+PkyZNoajo3x1ilUiE7O1vQ5jzDMLjllltwyy23APhkU/3gwYOYnp4mw63FYjHsdnvS95oKS2U58pGqAAAgAElEQVRcwFv3Pfjgg+jq6kJNTU3MUOx4NDY2oqqqiqTu77nnHuzfvz9GMK+88srop5wA8NlFP/lPIYuVduUFk+8nnpycxMjICORyOcrLy8m2RirEKypkWRZmsxlGoxEKhQJr1qxBZmYmgsEgOW+WZYmAsCwLo9FIUpsZGRkxAqJSqRat4CZVFuMam1145PP5UFhYiKysLEGFR9F/En0O4XBY0NjA6enptH7P6bIiin5SQWhKdmpqCu3t7XN6OReyRzH77tPtdqO5uRlVVVUoKioSfJxo4RV6x2cwGCCVSmG1WslFyBdIzTZN1ul0eOyxx9DY2Aiv14uysjKEQiF88MEHUCgUMBgMyMvLE5RGeemll/Dcc89BoVBAJpNhdHQUOTk5kEgkePDBBwW/ZyEsR/uKz+fDxo0bE0b0PGNjYyQjAADFxcU4efLkfE95CMDBRTnJTyHzVbumi1gshs/nw/j4OCYmJpCbm4tNmzYltIsU8v2KXh/C4TBGR0cxNjYGnU6H+vp6Uvw2ew0RiURkW8BoNBK3LD616fF44PV6yZCCUCgEsVg8R0hnR2OLfU0slXEBfyMupPBIiONRKBQSlJJ1OBwJB08sBatSMOcTPL6QaGJiArt27Zpz8SxEMKOFzmq1oqOjA5s3b075DmfLli3o7+/H6OgoWJbFlVdeOW90CZxz6Lnvvvtw6tQpMAyDbdu2ITMzM2HFsFqtxlVXXTXn/91uNywWCzFN4FszdDpd3Ojzo48+IsUC27dvR1dXF+666y7s27dvztzN1YDQ/ZZ4qfdEC80LL7wAAFsBXL6ws/v0kcqkkFRwu91wuVzo6OhAWVkZduzYMe8Cy68byTIsIpEIwWAQPT09pHF++/btSa/PRESnNmebsITDYfh8Png8HrhcLpjNZvh8PnAcR/YI+ZsMoXt6yViqPsxkx0zV8Wh6ehoOhyNuVBq9Z2y326lgzsd8KdlwOIy2tjZIJJKE478WI8LkK3ujBZlPOwhpv9DpdPjc5z4Hq9UKpVIpeAC2wWDATTfdlNa580QXx/DG6GazGZ2dnZDL5ST65NMtNTU1OHLkCBQKBWZmZlBVVYUnnnhiRY80mg+hgllcXAyTyUT+PTo6isLCwjmPe+edd/CjH/0IAPZxHBdYxFNdtfAtHJFIBOPj46ToSshCPV8hD98WYjSeq6tSqVQoKyubswDHg1835hNMvjfT7XZj7dq1qK6uXlJvY4lEkrDgxu/3k8pvt9uNtrY2Yk6gUqnm7BEKvQFZ6ggzHeIVHrW1tWHt2rVgGCZh4ZHP58Nzzz0HlmVx6tQpbNq0SdCNTbJivkAgALlc/kcAWwDYANzNcdwwsAoFM1FK1uv1oqmpCWVlZfNWbi5EMPnxPpFIhDQ6A8CxY8dw+PBhAMCuXbtw7bXXJv1S8nsA4XAYJpMJHMehoKAg7TvZdJhtjD67NUOn0+GWW25BR0cHjh8/jrKyMvzkJz9ZtWIJCBfMbdu2oa+vD0NDQygqKsLLL7+MF198MeYxra2tePjhh3Ho0CFUV1dbluqcVwvx0q58dCl0kZZIJHMilkgkgrGxMYyOjiI7Oxvr1q2DWq1Gb2+v4Gs5UWaK4zjYbDYMDQ0RYVepVHFvjmazVNsH0dEYfxPOF0Lxe4Qejwd2ux1jY2Ok/YvPBEWL6WwhW4oIU0jknip8RC2RSBIWHk1NTSE/Px8mkwm/+c1v8NOf/jSpQ5OQYr7f/e53AGDnOK6KYZh7APwYHxfzrbqVL57gWSwWnD17Fps2bUoanqcrmIFAAGfPnoVUKsWmTZvIxTIxMUE+fJFIhGPHjqG6ulpQpV8kEsGhQ4fIHXNhYSFuvvnmZRXNaFQqFTF0iB7Lddddd+Gee+5BRUUF8vLyzsu5LRZCBVMikeDXv/41rr/+ekQiETz44IOora3F448/jq1bt2Lfvn34+te/DrfbjTvvvBNtbW2nAYxwHLdv6d/FymK+tKtUKk3JaEQikSAcDpPnGY1GWK1WFBQUzGkLSXUKSfRjWZbFxMQEjEYjsrKySG+mw+GAx+MR/uaXmUR7hNGVqx6PBzabjRQgyWQyIqShUCjujMuFcD5EWCQSkZv9HTt24P777xd0XCHFfPv37weA5z/+5ysAfs0wDMNxHLfqBDP6IuE4DgMDAzCbzXH3K+ORjmA6nU60trairKwMdrs95ovm9XqJMTB/folaONxuN7xeLzQaDWQyGSYnJ2E0GklxiclkwtjYGMrTHBa9mPDRJ8MwaGxsREZGBioqKnD27Fn4fD5otVpiDLCaIs5UesZuvPHGOb2xP/jBD8jf33nnnegfbVqE01uV8ItwvGpXqVSaUlU6X33d09MDv99P2kLiLci8uAo9Lj8pw2QyYXx8HHl5ediyZUtM+4IQc5LlRKiwRVeuRvcZR/dTejweOJ1OeL1eOByOmGIbXlAVCkXavdCLidD37XA45uwNz4eQYr6xsTEAMH18HmGGYZwAdAzD+FbPSvcx/IfI+8HKZDLs2rVL8C85VcGcmJhAT08PtmzZQlo2osnPz4darcbY2BhEIhFkMlncilm+RxI4F8ndfvvtgs9huRgcHITD4UB5eTm0Wi1GR0dx5513wmazgeM47N27F0899RRJY1ksFvT09EAqlSIvL29Rp4osFYFAIG3jCkp85hMZqVQqSNT41g2bzQa/34/q6uqklo6pRJh87YHH40FJSQl27twZ90bv0+b0M7ufUiKRIBgMorS0NKbYZnbREV9sE53iPV+Zr/lItehHSDFfgu8yB+D7q04wgXOpzA8//BAVFRUoLS1N6blCLwiO49Db24vp6Wk0NDRAJpPB7XbP+TBVKhUeeOABNDY2IhKJYNu2bdBoNJiamsLg4CAUCgVqamrQ1NSEbdu2QS6Xk0kgV111FcrKymJSsqm0p/DnuRi8/vrreP755yESiaBQKPDDH/4Qf/zjH2G326HRaMig6y996UuoqKiAXq8nd7I+nw9ms5lMFeGjT71ef17HDiViJQv6pw2JRDJvhMlHfHxbSF5eHhmingyxWDxngsVsHA4HhoeHYbfbUVJSgvr6+nl//0L8ovkbRpvNFiMqK82kIB7R19l8Lj/RLSATExPwer1kX3F2VLrYEXkqa4HT6UwpwhRSzFdcXIzOzs4SAKMMw0gAZAOYBrBj1QmmxWKB1+vFpZdemnZjcrILgo9e5XI5duzYQaLXRBeTVqvFDTfcAODcyKE33ngDp06dIubuPT09CIVC5A5NJpPB5/NBLBZjz549mJiYAMdxyM/PPy93ccFgEC+88AIKCwshlUoxMTGBV199NeZC4L/A8S4OhUIRM1WEHw/W29sLqVRK9hoyMzMTXghLZVpAWXrmW9wSpWTdbjeMRiOcTieKi4tJW8jg4GDKadbZcBwHi8UCo9EIqVSK8vJyKJVKZGdnp9SHORveHMFoNEKtViMnJwc+nw/T09NkvzAjIwN+vx/j4+NEUBZyTS+1NV485msBiTYmcDgcGBsbg9frxalTp2Ls8hZyE5FK1a3dbk9JMIUU8+3btw9vvfXW5wAcB3AHgHe5cwvfpatGMDmOQ19fH6ampqBSqdJ2d0gmmLw7UGlp6Zxq22T7G/39/Xj99deJj6lEIsEll1yCkZERlJaWwmQyQSqVIhKJ4NprrwVw7qJP1R5wseGrG6PvPMPhMO655x68+uqrGBsbg9vtRnV1dYxpfDxm29L5fD6SunW73cjJyUFeXt4cU3QqmJ9OZtcc2Gw2Mhe2vLwcGzZsiBGEVPYlZz82uppWo9Fg48aNZL96enpaUPo23voQiUQwOjqK0dFR5ObmYvPmzcjIyEAwGIw5d36/sKWlBZFIBJOTk/B4PCQy40WE32uUyWTLnu2YPSkpVWYXHbEsi+bmZmzZsiXGLi/6JmK2iXuy955Kz6nT6UwpJSukmO+hhx7CF7/4RR3DMP04F1neQ54v+JXOI6FQCK2trVAqldi5cyeOHj2a9rHmE8zp6Wm0tbXNcQfiSZauGRoaglqtBsdxUCqVmJmZgdfrBcMwqK2thUwmw/T0NNavXy+obH25yMjIwK233opXX30VIpEIUqkU+/btQ2lpKb7yla/gs5/9LFiWxenTp7F79260tbUJKrACzkWffKsPy7Kw2+0wm83o6+sjhUV5eXmQyWRUMFcpyVKcHMfBZDLBZDIhKysLNTU1CSfdSCQSBALC2ll5MQ4EAhgZGYHZbI5bTQsI34qJflwwGMTIyAgmJyfnGBgk2gvLyMiARCJBcXFxzOcS3Q4S3U/IF97wIsoX3kRndFay0w9fzZpoTifHcQiFQsTpKN57jxZShUKRkvF6OqPFkhXzyeVycBx3Z7znrnjB5O3n1qxZExOJpfuLT3ThjIyMYHh4eN4xY8kiTJ1Oh9OnT6OoqAhDQ0OwWq2w2Wy48sorMTk5ieLiYlx88cWYnJzEsWPHyOSSvLw8Qb6JS8nf/M3fYOPGjbDb7aiurkZRURFYlsW3vvWtmJ46k8mEtrY27NixI+XXEIlE0Ol0JM3j9/thsVjQ29sLp9NJGt31ev2SpKaFOJJQFg+/34+RkRF4PB4Eg0FB00IkEongto5AIIDp6Wk0NzejtLQ0oVkJILxAiB8S39XVRfY9o3uuhcDfJESvT4naQfjCG4/Hg5mZGeK9Cpy72eQFabHM3Bc7k5MsfcowDGQyGWQy2ZxIMBKJEKcj3uGH3yvlOA79/f0x6d1Ea8JyRukrWjAnJyfR3d2NzZs3x3zRhNpcxWO2YHIcR1olEk0a4Uk0rYSnpKQEBQUFMJlMqK+vx6WXXgqDwYDu7m5IpVKsX78eAIhg8J6KHR0d8Pv9pOhBp9Ol9KVejC+M2+1Gfn4+LrroInI8p9NJFi/+vQeDwaRpWaHI5XKUlpaitLQULpcLZ86cgdPpRH9/P+mzysvLQ1ZW1qK8R7/fT4dHLwGzfzdOpxPDw8PEx1itVqOiokLQdzpZSpafGDI0NETqAnbu3ClobzJZqtflcmFoaAgejweVlZVYt27dggZWCyFR4Q3fV8nvEUabuc+uYFWpVIKjrKUQzHSPJxaLifNYNFarlVS/er3emNQ277+rUqnQ0dFBboSEaoEQl5+//du/xZ/+9Kd+RLn8MAxzLYB/W5GCGa9CNRohNleJiE6rhkIhNDc3IycnZ87k9WTPnU1PTw/efvttMAwDrVaL22+/HRKJBK2trbjoootIS0k0SqUyxihgamoK4+Pj6OjogEqlItGn0PRnuvz5z3/GT37yEzIz8Oc//znkcjkyMzNRWlqKmZkZsths376dCP9iI5fLsX79eqxfvx6BQAAWiwX9/f2YmZlBdnY2qaBMty1kKeb2Uc7BsiwptJHJZGRaCMMwGBsbQzgcFvR7SySY0RNDlEolqquroVAo0NraKkjU5quotdvtGBwcBMdxqKiogMvlIlN5ol/f4/EgIyNjWdqS+BRnZmYmFAoF6R3kOA6BQICkOKMrWKVSKTIyMkgdQVZW1pxpIEuVkl1MIpEI5HJ5TDaKJxwOk4j8/fffh8ViwY4dO/C9730Pe/fuTXpcIS4/OTk5iOPyMwVg74oTTH5cllqtTnjnmOpMzGj447ndbjQ1NaGmpkbwfmKilCzHcXj//fdhMBggk8kwNTWFt956i+x7qFSquGma2e+JF0iO40hfVHNzMyKRCIm2kvWmpcrk5CR+8pOfQKPRQCqV4sSJE3j11VdRV1eHRx55BFarFVlZWZDJZNi5cyeef/755AdNg9l3vhkZGSgpKUFJSQmJKiwWCwYHB8EwDPR6PfLy8gRVPvJQwVwaOI7DyZMnkZOTg7q6ujmfMV8pm45gRk8MmT2NhB8TJoTZKVm+knZ4eBhyuTymoG3298nv9+PNN9+E2WyGRCLBNddcQwTMbrcjHA5Dq9US4WAYhrjpxIv8wuEwJiYmAIDMrE0Ey7Joa2vDW2+9BblcjmuuuYbcREeLic1mw/DwMN577z34/X7IZDJs2bIFEokkJirzeDzEcm8x1pGF+sjGY749TIlEgqysLGRlZeELX/gCLBYLXn31VUHHFery8y//8i/8P6NdflqBFZaSdblcaG5uJntoiUhlJmY8QqEQmpqa5qR6k5EowuSNpnlBHR0dBQDcdtttMWbsqQxv5b8U1dXVCAaDsFqtGBwchNPphEajQX5+foyjR7o4HA6yzwCcW1jGx8fx4x//GG63m8z9e+ihh2I2xheb+VJFfNSu1Wqxbt06MhB6YGAAMzMzyMrKIsYJ8y3KXq9XkDk+JTVEItG8aVGh5gXAJ4LJ2+JNTU2hqKgo7jSSVFx5+K0YlmUxPj6OkZERaDSauAI/m46ODlgsFhQVFcHv9+Pw4cP47Gc/i1OnTqGpqQkMw6CwsBDXX389ZDIZxsfH0djYCJZlcdFFF8XsrYbDYezfvx+Dg4PIyMhAeXk5brzxxpj3ZrPZcOTIEXg8HkQiEQwMDMDv98PhcODEiRO47777IJVKUVpaCr1ej6amJpw8eRKnT5+GSqXC5ZdfjpmZGQQCATQ0NMREZXzLi8lkihl6HW1QkEqKdakEU8iNbaqmBUJdfqKieeLyg3MR5soRTN5R5+KLL066R5aKw0c0/OivQCCAyy67TNBE72gSLQgikQjbt2/HX/7yF3R0dGBmZgZXXXUV/u///g979+4lJdTpNvjy7kFFRUUk2jKbzejv7wfDMAiFQnC5XGm57JSXl5N9Vz59U19fj2eeeYbsLUgkEnR2dqZ17kJJZW+FHwhdXFwMjuPgcDhgsVjQ2NgIjuNI9Dk7GqcR5tIxn3glMy+IxufzYWZmhlhRLubEELvdjuPHj8NgMMQtQOI4Dl1dXWhsbIRKpUJdXR28Xi96enrg9XpJS0Zvby9effVVdHV1oba2FiKRCCdPnsSpU6eQnZ2Nnp4eXHXVVVAoFGhpaUF+fj6qqqoAAJ2dnfjLX/4CtVoNsVgMl8sFr9cLi8UCrVaLa665BgcPHiSV9h9++CFsNhtKS0tRUFCA48eP4+mnnybR40033YRTp06hoKAAvb29pAUmPz+fWHRGR2UzMzPIz89HdnY2uTGJHqvFv0+5XB6zR6pUKuNGfUvRDsbvVSZjenp6OV1+AKwAweQ4Dt3d3XA6nXH3K+ORTko2EongzJkzYBgGKpUqZbFMxsjICNrb2zE2NobS0lKUlJTAZDKht7cXGzduXJBgRhMdba1fvx52ux2nT59GZ2cnvF4vdDod8vPzE863nI1cLsezzz6L3//+93A4HLj11luxefNm5OTkYGpqCgqFApFIJK2q2FRIt3iAYRjk5OQgJycHa9euJdH40NAQHA4HsrOziXFCKoIptDigubkZOp0OjY2N5fwIoAuR+b7fyfxk+bFdw8PDpK1JSCGPEAKBAIxGIyYnJyGVSlFQUIDOzk4YjUbs2rUrpg2isbERr7/+OhwOB7xeL0ZGRjA4OIjJyUl0dXVhYmICNpsNoVAIPp8PLS0tCIVCUKvVaGtrw8UXXwylUkkqg/l+Q5fLRV7jxIkT5Br2+Xw4efIk/H4/NmzYAKfTiVdeeQUASEeATqdDX18fysrKMDo6iuHhYZhMJgwODmLz5s2orKyE3+/HqVOnMDY2BpfLBa1Wi4yMDGzevDnuZ80wDI4fP45jx45BIpFgz549WLduXcxj+PFiXq+XFB5FIhHSU8m3kAQCgSWJMIVUyafqIyvU5cdkMvFtQdEuP2AYpvi8CiZfdJOdnY0dO3YIvkBSTckGAgE0NTWhoKAAFRUVOHLkSLqnHIPP50NfXx/MZjP++Mc/kgsGOGdikJ+fT3rKFkswZ8NXzO3YsWPOfEuFQkH2RedLRebm5uIb3/hGzP/96U9/wte+9jWMj4/j6quvxuc+97mYnx86dAg//elPoVar8cQTT8TsA6TDYt2pzo7GnU4nLBYLDh8+jH/+53+GXq/HiRMnsG3btoQXeirFAf39/Xj55Zdx7733khFAlFgSRZjR6dHoiSEfffTRgsXS6/ViaGgITqcTZWVl2LRpE06cOIEDBw5gcHAQZrMZubm5+OY3v0nmLj7zzDOw2+1wu90oLCzEm2++idLSUtTW1iI/P58IZE1NDfR6PZxOJ6ampoiQqNVquFwuiEQitLS0oKysDJFIBAqFgngYZ2RkIDc3FzabjexzFhYWQiwWQ6vVYnh4GBqNBna7ncy6vPTSSzE5OYmxsTGEQiEYDAZkZGSgsbERV199Nex2O7q7u6FWq+F2u5GdnY0bbriB2IZyHIe2tjYYjUYEAgGEQiEcPnwYJSUlCAaD2L9/PwwGAxGfaKefaKJ7KvlRgLwhxGybQD4oSef3KDTCTDUlK9Tl5/nnn8euXbuAKJcfhmE0AA6cV8FsbW1FaWlpyk38qaRk+UkjGzZsEDyoWQjBYBD/+7//C6PRCKPRCLvdjszMTGi1WgwMDGB6ehrFxcVkg3k5eoVmz7d0u90wm81obW1FKBSCXq9Hfn4+cnJykp7PmjVr+DE3ZCg3z/Hjx3HnnXcSU4ajR4+iu7t7QZ/vUqR2GIaBRqOBRqNBTU0NbDYbDhw4gN/85jdYs2ZNwj3gVIsD7rjjDtx7771X8yOAFvVNrBKS2eP5fD7y72AwSPxj400MSZXo2gCn04mhoSEEAgFUVFQQJyGv14vh4WGMjo7CarWCZVk0Njbi0UcfxeWXX47169fD5/NBpVKBZVmcOHECNTU1AM7dGLtcLlKtWlJSQuwgq6urUVpaiuzsbFLct2HDBjQ0NIBhGJSVlUEikaC7uxuBQICkNrOzs8FxHC655BJYrVYoFApiE3jdddfh/fffh8fjwfbt27F27Vo4HA788pe/hN/vJwGDRCJBUVERurq6cPnll5P9xJycnBiP7ePHj+PAgQPIysrC8PAwJicnwbIsjh8/DovFApFIhD179iSN1uL1VJpMJrLu8BFp9JxO3pt6tjHDfNc6/96S4XQ6UZ7CZCehLj/3338/4rj8fBFA1XkVzG3btqUlJEJTsuPj4+jr68PWrVsX3RjAarWSfsErrrgCUqkU/f39pJDglltuQV1dHfliLVWEOR98j9OaNWsQCoVgtVphNBpx+vRp0qaRrFDGZrPhiSeegNlsxt69e/GVr3wFBw8eJGPNgHMLVmNjI26++ea0z3U5rPH4veavfe1r8z4u1eKAjy/umOIAyidIpVLiehVthD6fIYDQAjnexpEXSrFYjIqKCnLdcRyHmZkZEjWdOXMGZrOZ2Np5PB6IxWK8++67WLduHYaHh+Hz+SCXy7F371688cYbxKHo7rvvRnFxMV577TVMTU1hzZo12Lt3Lxl9d+LECbAsi5qaGuzatStuVmfLli3YsGEDjEYj5HI5tFot2traMDIyAoPBgE2bzk2Ju+mmmyCXyzE+Pg4A2LRpE+6//3788pe/BHDupqOyshLl5eUoLS3FxMQEdDodxsfHUV9fH/OaLS0tyMvLI1WyY2NjxBlJo9HA7/fj6NGjuOiii8h+amZm5pyWjnjw1nf8TUA8YwbenCB6IgqAuPukYrEYoVBIkGCmGmECwlx+/vznPwNAVfRjOI77VwD/el4FM92oK1lKluM49PT0wOFwoKGhIW4+fCFl1RzHkT0yfkxQVVUVduzYgdzcXIRCIZw8eRJ9fX3YsWMHNm7cSJ53vpBKpSgsLERhYSFJVZrNZpw8eRIMw8BgMCA/P3+OQfq9996L5uZmyOVyPPXUU/D7/Whvbye/A74hfKF+uMshmEL3MBejOIDyCX6/H5OTk2R03Pr16wWN7Uq2aPKDq0+dOoXMzEyS0o1+3WeffRY9PT0IBoPIzs6G3W4nacmMjAyEw2EoFApotVqwLIuqqiqEw2HSZvLVr34VHo8Hcrmc2N196Utfgt/vj0k56vV60gfY0dGR8FoXi8Wora1FbW0t+b9NmzbFOP44nU6Mj4/D7/eT/tVQKIS6ujr80z/9E44fP46srCzceuutMBgM2LdvHw4dOoTJyUls2bIFu3fvBvDJnFI+1csLplarhdlsxuTkJIaGhlBWVoauri5YrVY8/fTT5Abjvvvuw8UXXzzv7yBZlWwicwKO42IGXkd7z/p8PgwODsZEpfHW8FT3MBeD8170kw7zRZjhcJj4zibaF12IUxDHcWhuboZGo8FnPvMZtLa2guM4rFu3DpWVlXA4HHj33XeRm5sLsViMI0eOQKfTnZcIMxHRqcq1a9ciEAjAbDYTg3StVou8vDwolUqcOXMGSqUSMpkMwWAQv/3tb2EwGEhREMMwePTRR8mdcbosRQP0bLxer6A70lSLAz5umSDFARci8W4o+D5HsVgMhUKB7du3CzoW34aSSDB5k3WTyYRIJIKNGzfOWThdLhf+8pe/oK2tDV6vF729vRgbG4NWq4Ver4fL5SL7hGazGbfffjtEIhE++ugjNDQ04K677kqYspfJZCkPxk5GIsefkZERIuoulwsGgwHXX389eY+8EN58882Qy+XkpvP48eN46aWXEA6HsXnzZiiVStLuJpfLkZOTg9HRUcjlcphMJqhUKrz44ovwer0oKSmB3+/HSy+9hPr6+nmvy4UYyPBtLPygBuCTbJVOp4PH40loYO90OlOeVJJKId/AwMBJfOzy8/H5fgvAQ6tSMBNFmF6vF01NTSRNMd/z01mg+cqxyspKMsmkrq4OLMvizJkzePrpp+FyuWCxWHDbbbdBKpUSH8ilEszFOGZGRgaxqIsez9XV1YWMjAzY7XYwDEO+5IWFhSgtLYXT6YRMJsP3vve9BZ/DcgmmkHmjqRYHfFzZ+K7Q/UuGYd4FwF/p6wDcz3Hcn1N6MyuUaDHjjQwkEgna2toEHyOR208oFMLIyAgmJiZQUFCA7du3o7u7e46w9vf346mnnsKZM2fI/mBhYSGpcJXJZNDr9VCr1Xj44YdRXl6OSCRCmuE7OjoE9WcnyjLWzYEAACAASURBVFIt5rUuEokgl8uRl5cX8/8sy5LJIHytAp/q9Pv9+O1vf4v8/HyoVCqcOnUKDz/8MKqqqtDb24vGxkbk5eVheHgYwDnP2tLSUhiNRkQiEVKlGolEkgqiw+EglcKL4f/MrzN8J0A00Qb2R48eRWdnJ/bt24cbb7wR//Zv/zbvcVMt5GMY5uf42OWHYZgNOLeXWbsqBZPPc0djs9lw5syZhJNGoklnqvrMzAxaWlogl8tjxn5lZWXBbrfj3XffRVFRESKRCHp7e9He3o6qqipwHIecnBxMT6+O4CN6PFdtbS2uueYa/Nd//Rc4jiNuRBMTEygsLITX641bup4O/F7IUiI0JZtKcUBVVRX/fXss2XF5OI67CgAYhvn/AFwJ4C9pvqUVQygUQn9/P5kYsm3bNvL7ZFlWsHEBMFcw/X4/hoeHYbPZ5ux9zh4fNjMzg9/+9rcYGBiAyWTCzMwMOI6DVCol82YNBgMKCgqwd+9eKJVK6PV6lJWVkcKjdNaHaJYjmyQSieKmOlmWRWdnJ+mp5iOxxsZGMpLsoosuQktLC0QiEWQyGaqrqzE9PU3M3+VyOerq6nDDDTeQTEFOTs4cQfzggw/wi1/8AkqlEqWlpfjGN76RkhFMPKLHDM4m2sD+H//xH/HSSy+hpaVF0HEX4vID4BYAL3McF1i1ghk9AshoNGJkZAQ7d+4U5OSS6gXBR1tZWVl49dVX4fF4cNlll0GlUiEcDpMCAolEAolEgg0bNpB0w6WXXorc3FziVbnaePPNN0lKlmVZOBwOrFu3Dr29vVi3bh0MBgN27NgBuVyOf/3Xf8Wll16a1uuspD1MIKXiAJ7BVM6FYZi/BbAHwO0cx6VvW7VC4Nsn4k0MScWRB/ikkMftdmNoaAhutxvl5eWk/WP2YyORCEKhEH71q1+R/kKHw0EeI5FI4PP5UFBQgOrqatx7773w+/0kUzJbCFJZH+JFmYspmKnWWohEIlRWViI/Px8ul4vcINxwww3Iy8tDW1sbCgsLce+996K4uJjst9psNtTU1KCiogJGoxHFxcWor6/Hl770JbLv+e1vfxsFBQUAzl1Lzz33HCkeHBsbw6FDh3D33QvrrBJaIct/vnxEmowFuvwUATgBrNI9TD4ly7Iszp49i0AggF27dgl27E/lghgcHCQR1Ysvvgin04nu7m7S1ykSiVBRUYGysjIMDAxAIpFAo9HggQceiMnNr6Q9zFRQq9UkJcuyLLRaLfbv3w+WZfHee+/h3nvvJf1kd955J9566y3U1dWlXFC10gRzKWEY5k4A9wG4heO4xdsIO48olcpFG4QeCoXQ29sLqVSKiooKUgMQD4lEAq/Xi7/+9a84cOAAKisrY4wCgHOL6+bNm1FbW4v6+nro9XoUFxcnXC+ErA+hUAhjY2OQSqVQq9VJWyWWE6VSia9+9as4ePAgfD4frrjiClRUVAA493mVl5ejoqIC11xzDTiOw/T0NB555BFyo6JSqeBwOPDDH/4QgUCA9I3+7ne/w0033YT9+/ejv78f/f39qKysBMOcmwNqsVjw/PPPY3x8HA0NDbjssstSXgdSGR4NCC8cXWAhH3ngqhRMfvLAyZMnodPpiJOOUIRcECzLoqOjA+FwGDt37sSxY8eQkZGBzMxMaDQafPjhhygvL4der0d/fz8uu+wy1NfXw+/3o6amZk5J9moVzKeffhp33HEHMXF++umnAZz7DLu7u8GyLClUCAQCePfdd2Gz2aDRaMh0ESF7GxeKYDIMczOAfwRwM8dx/vN6MsvMfNESx3HEoSkcDsNgMKC6ujrpMcPhML71rW+hpaUFbrcbk5OTc+obOI7Dpk2bUF5ejo0bN6KkpGTe9WK+9SEQCJD0cF5eHrGU4/cPlUolvF4vpqenSbHTQnqw063mz83Nxf333x/3Z9HHYxgGOp0OV155JT744ANkZGRALpfj/vvvx89+9jNotVpEIhG4XC4cPHgQr7/+OkZGRsjMTpPJhHA4DLlcTtyQlEolabG58sorUzpvoYLp8/lS8oVeoMvPKIASYJUKZiAQwNjYGDZt2kRSBKmQTDB5ByKtVovq6mrypfL7/QgGg2hubsbExAScTifpYwyFQklLsFejYF599dX47//+b8jlctTW1sZ83lVVVaQ4gN97uO6667B+/XpSONTX1wepVJp0UPaFIpgAnse5i/DDjxeu/8dx3O/O7yktnGSLeqJWEZZlMTExAaPRiOzsbNTV1cFutwuuQH3uuefw/vvvE3OEycnJOXughYWFOHLkCP793/8darUad9xxB5588smExSzx1ge/34+hoSHY7XZiWMAPOubfO1+I09fXB6/Xi4GBAfh8PmLHGf1HLpcvi5mJUB566CGsXbsWFosFdXV1WL9+Pa6++mocPHgQbrcbnZ2dpACQr9oNhUKkPee6667D888/j4KCAlLlfOzYsSUTTLvdDo1GI/i4C3T5eQ3AiwzD/GzVCabZbEZvby90Ol1aYgnML5herxenTp1CVVVVTEUl797x5JNPkikD7733Hnw+H3Q6XUx+PBH8tJG8vDzk5+cv2mDkpb7wdDodLr744jluLNdddx2++MUv4te//jUkEgl+9KMfkU306Fl2Pp8PZrOZDOrW6XTIy8tDbm4uEckLRTA5jkveDb5KEeInyy+G0WO79Hp9jNuPy+WKcQaajw8//BASiQRqtRoSiQQulwt6vR7T09Nk8a2qqsLJkydJ3+VLL72EW2+9FQ0NDXGPGb0++Hw+YrFXXl4+71BpvhBHpVLBYDCQBT1RjyU/8zL6T7p2cgtFIpHgiiuuiPm/+++/H4WFhfjRj36EtWvXAjhn2BIOhxEKhSAWi8EwDO644w7ceOONOHDgAJkIwwtrY2MjZDJZzHtM1FcJpCaYqZgWpFrIB+Br+Njlh+O4swzD/AlA56oRTI7jMDAwALPZjPr6ehiN/z97Xx4eVXl/f+4smSX7ZJ2sZAdCQtgJVEBAqq1C1Srauhe3r6it/kDqTqutSCm2FQW1olJUEKWCIJsWFIEsJGQhIWRfJjNJJpl9nzv39we+rzPJJJnJBijnefI8hMzMfe/M3Hvez3ZO85Bfqz+brp6eHpSVlXnttOXxeLjqqqvw6aefYs6cOWBZFlVVVWAYBjfeeOOAVlvkCxQREYFZs2ahs7MTtbW1VCg5NjaWzm1eihioff6ZZ57B008/TX/3BiIjRtr3u7u7oVKpcPbsWWqUbbfbfxKE+VMFIUw+n4/m5mZ0dnYiLi7Oq21Xf2Ml3hAREUEdgkg3rMPhAMMwSExMRGZmJk6fPg0+nw8+nw+RSAStVovu7u5+X5PH48FisaCyshIGgwGpqamDii24o/fGob8ZS5ZlqS6rRqNBW1sbFTMn5GIymWjT1FgTqUAgwM9//nPs3r0bOp2OCpYAF7J8DMMgJiYGS5YsgVAoxJo1a7B+/Xro9XpMmzYNTz75JLUHJLJ57nOVQqGwz4bBV8L016kE8LuRz2NomOO4lwG8fFkQJsuyKCsrA5/PR35+PlWEGCq8CR8oFArU1dVh1qxZ/d5URSIRRCIRjh8/DrVaDYfDgQceeKDPjJQ7HA4HbelOS0vzMEZ2uVyUPKqqqhAYGIjY2FjExMSMuJvKcDDYxerPheyud8txHJ0hU6vV1Ok+JibGJ71bf3HFD3N0MVCEyXEc6urqYLVakZSUhPz8/H43SL4SJsdx1GA8ICAAVqsVNpuNNqERcXCbzQYej0ddRoKCgvp13zGZTFCr1ejs7ERWVhays7NHjaj4fD613XKH0+mkRGo2m6HX69He3k4H991/RnsUCwBWrFiBF198EVqtlvplulwuej/cunUrcnNzMXfuXGzduhUmk8nD2J08rncQQojUZDKho6MDJpMJFosFfD4fFovFwxWl93nqdLoxV/kBLoMaptVqRXFxMeLj42mn11D9MAncI0yO43D+/HloNJp+ZfQI+Hw+4uPjcfjwYYSEhEAmk6G6uhq//OUvaXrCHSS9m5mZiY6Ojj43Ex6Ph6ioKERFRYHjOKq1WFRUBI7jaOq2t1zdWIPjOBw9ehT79u1DYmIiHn744RGJ1BiGoTtvjUaDjIwMqjd65swZ2jgUHR09IkPRLMuOyOtcge/Q6/VoaGiAVqtFXFwcpkyZMuh3eTDCdG8QYlkW48aNA8MwaGxshN1uh1QqpWldkuIkGYzY2Fh89NFHfYwCjEYjGhoaYLFYEBwc7GFi4C+G2+DnrstKzic6OtrDKaSrqwtNTU00zU1SweRnJL/n06dPx5tvvonf/e530Gg0VGGJiFSsX78eLMsiJycHH3zwgU8atAD6CLkDQGNjI8RiMSQSidfzJFFoSUkJgoOD/Y68e3p6sHz5cjQ1NWHcuHHYuXOn10iVYZi7ATz7/a8vcRz3PsMw0kuaMLVaLc6cOYPs7GyPlOdQ/DDdQZ5PIleBQICZM2f6lBLkOA4LFixAdHQ0BAIBCgsL8dprr0EikeDqq6+mNTytVovS0lKa3u3s7BzwImIYhu42MzIyqFzduXPnYDKZEBkZSX0ux6J9nWVZFBcXw+Fw4JtvvsG//vUvOJ1O8Hg8fP311/jiiy9GlMSJcEFYWBjVu9Vqtejo6EB9fT2NTGNjY4dklH0Fow/ymZBRhcbGRjAMg9TUVISHh3vdVHpDf4TJcRxUKhWampoQEhKCnJwc3HTTTTh58iQ4jqMGzzweDwKBgKrU2Gw2iMViasm1ceNGrFq1Cnl5eTAYDKivr4fdbkdaWhpkMhkaGxt9Irz+iHG0OuKFQiGVtHSHw+GA0Wj0iNRIyrM3kQ4ViYmJ2LRpE+644w5YLBZq9QVcICGJRILCwkI8+OCD+Pjjj/0aDXGH0+mESCTq9zxJU1VZWRlUKhW+/PJLnDx50uf7wSuvvIJFixZhzZo1eOWVV/DKK69g3bp1Ho/5XmTmBQDTcWGs5PT3jT+XrnABSZHOmDGjzwftrx9mbzAMA5vNhlOnTkEul1P1B1+QmJiIsrIyBAcHo729HWq1GvPmzQNwYcg/JiYGTqcT1dXVmDlzpsfa/bmI3OXqSN1PqVSisrISQUFBNHU5kqipqcHtt9+OlpYWBAcH01SWyWSiFx/HcSgpKYFKpRpy05U39G76YZgfjKHHjx8Pq9VKBSRMJpNH49ClWvv9qcGd0KRSKbKysmjdzmKxwG63+/Q6vQnT3TdTJpNhypQpEIvFAID8/Hw89thjqKmpwalTp9DZ2Qm1Wo3w8HB0d3fDZrPB6XSCZVkolUr6/b3nnnvw3HPPUb1Zo9EIqVSKKVOm4L777vMwVO7vXJ1OJ/3eMgxDv79jPUImFArpteK+PnciVSqVNDotKyvrk9r1dg21tLTgmWeeQXNzM9LS0tDZ2UmdTIxGI92kEAgEArS1tdH69FAwUA2TKP1Mnz4dkydPxmOPPUYF733F559/jqNHjwIA7r77bixYsKAPYR48eBAADnMcR4yjDwO4luO4jy45wuQ4DufOnYNer+83RTrclKzT6URTUxMmT57sE+mYzWZ88cUXaG5uBsMwyM3Nxd69e2E2myGXyxEQEEAvmOrqagDAnDlzPPLuw7mIetf99Ho9VCoVCgoK6IVrMBj6NBW4r/+FF15AWVkZlixZgj/84Q99LhCXy4WFCxfSm0p3dzf19zSbzRCJRAgMDKTv+0jbpQ2mJUskCZOTk2ntlxCoRCKh0eeVGuXFA5Gimzx5cp/PQSAQwGQy+fQ6pEbGsiza2trQ1taG6OhoTJ8+vU8tSyAQIDs7G/fccw9YlqXZiDNnzmDVqlUwmUz05k4UuZRKJUJDQ7F9+3ZUVVWho6ODzhW2tLTgf//7H/75z3/i17/+dZ+1cRxHO0FJMw7JdpFrg7iEsCzrQaRDwVCbfRjmgneluyary+XC6dOnMX78eEqkCoUCJpMJLpeL2m0FBgbCarXimmuugVarRVBQENXXJZZoRHqPvG8ulwsxMTGU1IYKX5V+hmLtBYBKNwKAXC5HZ2dnn8coFAoAaHX7rzZcUPu5tGqYJDcdFBSEmTNn9vtFGU46rqurC62trUhOTvY5Qvv0009RWVmJ6OhoFBcXg2VZzJw5Ey6XC4cOHaLmyaTl+qqrrupz8x+pFCLDMLS+kZWVhZ6eHpSXl6OqqgoWi4WmbmUyGb1Qly9fjq+//hpWqxUnTpxAd3c3/vrXv3q8rkajgVqt9iB10gknEokQEhJCd+ovv/xyv+Q8VAykIdkb7rVf4Aej7DNnzsButyMqKgoxMTGQyWTDet99qXecOXMGDz/8ME6dOnUWAAvgZY7jdgz5oJcxkpOT+609+uPu4XQ6YbPZcPLkyX47aQncN898Pp+aPjc1NSEoKAgJCQmw2Wyoqqqi3bMsy0KtVqO8vNwjW0X0ku12O7Zs2eJBmO5ECcBDChO48P01GAyorKxEaWkpxo0bh3nz5iEgIKDP65Pv5FgrA5GUNWnCIbVGcm6kCaexsRErVqxAZ2cnBAIBtFotjViTkpI8zCSio6PB5/MhFosRGhqKP//5z8NK/frqhTmQtdfixYuhUqn6/P/LL7/s0xoGsu67ZAiTNMikpqb6NNM4FDQ3N6O1tRVpaWl+pfHOnz+PhIQE6u1WV1dHd1G5ublwuVwwGo245ppr+pWDGq00jUgkglQqxcyZM8GyLLq6uqBQKFBRUYGQkBDExMTgwIED9GKxWq3YsWNHH8IMDw9HaGgourq66Hp5PB6NXI8ePQqz2YzIyMghp1sGwnDcStyNsp1OJ90UlZeX0/dAIpH4XVfxpd4hlUrxwQcfICMjI5thmDhcqHcc5DhO6/1Vf5rwpfPVbrejqakJXV1dYBhmQINpgv5mqq+++mpcc801OHjwIL3hk2Y/8njS6e4+tsFxHEQikQfJ9SbK3te3wWBAQ0MD9Ho9/vjHP6KrqwscxyE3Nxfbt2+HQCCAy+WiKczeESk5j9EmUm+zzocPH8aTTz4Jk8mEq666Cg888AAeffRRNDc30+yVu+iE1WpFeHg4Hn74YcjlcrhcLsyfPx8AIJPJaKp8qPA1whyIMI8cOdLv84h5hFwuh1Kp9NrY9b3EozsJJQA4ClwihKlWq1FRUYG8vLwhhdmDgeM4GoHl5+dDoVD45WWXnJyMxsZGREVF0VrAoUOHqBRXXl4ennjiCeTk5PT7Gv3Nfo4k+Hw+YmNjERsbS02iVSoVgoODodPp6MXuzeKKx+PhyJEjuPnmm6FQKDB//nwsWbIEABAfH0+GeUcNIzVnJhAIIJfLIZfLPdLXv/3tb9HU1IS//OUvuOuuu3zSPfWl3kEimu/PoZ1hmE4AUQB+coQ50Oc3UITprqKTnJyM9PR0nDp1yifi8HZMjuOg0Whw6623YsmSJfjPf/6DI0eOUI1Z0hBDbp6kW9tqtUIqlSIoKAj33nsvVbAix+l9LNJZ63Q6kZqain379kGlUtFaf0VFBU6dOoX58+d7LYEQ8nQnUvfrgNwzRlrI3eVyYdeuXTh+/Dg+//xziMVi6HQ6/Pe//6XiA4TAyfHHjRsHmUwGh8OBRx99FHfffTfUajUUCgVsNhtN7wLwGAcJDAz0Sx6QbOwHw1DHSoiaz5o1a/D+++9j2bJlfR7zvd/oEoZhCBktAfBH4BIgzKamJrS2tvrsNOIv3FuQp02bBoZh+ridDIZbb70Vu3btQmlpKXg8Hn7961/j008/hVqtxoQJE2C323Hq1KkBCTMqKgrV1dWor6+npDaa9TaG+cEk+rPPPsOyZcvAsizEYjEeeOABnD17lqZuyZc5NzeXCiocO3YMEokE8+fPx/Hjx0dtnaMJ9/T1jh07cOeddyIxMbGPOHd/8KXe0et4MwEEAKgf5tJ/dPBGmCT9ZzAYkJKS4qGiMxSTd47joFar0dDQAIlEguzsbAQFBaG6uhrHjx+nGROGueC3qFAo6KjRtGnT8MILL6ClpQVxcXEQCAS0+a2316PJZEJ9fT0cDgc0Gg02bdoEp9OJ3NxcGI1GGI1Gqsna3d0NhUKBuLg4GsFu2rQJ7733HmQyGdavX49x48ahsbERCQkJkMlkNLJTqVTo6upCW1sbDh48iOzsbGpsQH78iUYJGa1duxZvvvkmrT+S95rjuD73RR6Ph/z8fGzfvr1PMEMaAcm4H3BhI2CxWGA0GmEwGKBSqUZFHpBsevzFmjVrcOutt+Lf//43kpKSqFBBcXExNm/ejHfeeYcQ8Z8BFH3/tD9xHNfDMEzCRSVM8ubOmTNnVDodLRYLioqKkJKS4pHm9TfaCwkJwX333YfCwkJ8+eWXiI+Pp4P1WVlZkEgkaGxsHPA1SNOO2WyGUqlESUkJWJYdcZk8b1iwYAGUSiU6OjoQHx8PHo+Hrq4utLS0oKysDGFhYYiNjaVt9wsWLIBarQZwoXnpkUceGZV1jSXMZjPCwsL6CFIPt95BwDCMHMA2AHdzHDe6qYRLFAN9f91TpySFabVakZqa6lUcgKRwfbkvEJGChoYGBAUFIScnx2NO+MEHH8Tp06dx7NgxREdHY+nSpdi+fTtYlgWPx0NISAiqqqrAsixuuukmmpkgGSSj0Ui7Nx0OBziOQ3JyMmw2G26++WZKPCdOnIDNZqOCHFKpFP/3f/8Hm80GgUCAuXPn4vrrr8e6devAcRwUCgWWLl3q0W37+9//Hnl5eWhoaEBiYiI6Ozvx3HPP0Shzw4YNuPHGG+FyuWC1WnHkyBEqck7uIf0RKekT2Lp1K+1P4DiOpobdy0bk+TNmzMDevXu9fg7k/ev9OXsbYSE6u0ajcUB5wN5Rdn+f91ARERGBr776qs//T58+He+88477Md4F8G6v47ZdVMLk8XiYMGHCkJ8/0BtL5iBzc3P7DNIOdY4zKioKNpuNkgkp+qtUqj46jP1BKpUiLS0NaWlpcDgcVKDcYDAgIiKCyuT5s3P0hWilUqnHTtA9banRaOg6du/ejba2NnrDOXHiBBYtWoRFixb5vJ5LEf3J4g233gFcGM4HsA/AsxzHnRqZFf+4wDAMnE4nTp8+DY7jkJqaOmBKjVhNDaR4xXEcOjo6YDab0dXVhdzcXK+fsUQiwbZt21BbWwuGYZCeng6pVIo333wTgYGBHmROyMZ9TIMIqZOueODC/WXPnj2089ZkMlECkUqlVK2HEL/dbsfXX3+N0tJS2O12SCQS8Pl8dHd3exDA2rVrAVzoCicNQ0TWz2az4U9/+hOWL18Oq9WKpUuXor6+noqcHDp0iDbjeauPkvWRyMx9bpYcg9R0Q0ND4XK58OSTT/a7afEnA9Cf4TXR2TUajVSVqaioyEMe0F3thwQ73lLkvmA4wgXAJZCSHSrIl9zbB6ZUKlFTU9NnDpJgqPXEcd+LL587dw533HEHHaxftGgRbrrpJr9fTygUIiEhAQkJCXC5XFCr1VRjNTg4mM5ajqY6DUlPyWQyTJgwASdOnKAdcWRDYrfbL4qW5UhiKDqyvtQ77HY7brzxRgD4gOO4T/o84CeE/uqJPT09aGhogN1ux+TJk30aOxioSYjMezY2NiIsLAyBgYEYP378oDfvkJAQmo5/9NFHsXfvXvT09IBlWcyaNatPZ77FYkFDQwPMZjMlePe/6/V6vPnmm9BqtfR+4nK5aDcu2SQQsCwLjUaDkJAQuFwuGo32PjdybIZhYDabIRaL6WPNZjNWrlwJmUyGuro6OrqiUqmwb98+3HPPPV7ro6QhkGEYPPfcc/j9739PjxUeHo7Nmzfj5MmTOHDgALq7u8EwDObOnYvFixf3+34SMh8O3HV2SZduXl4enE4nJdLu7m60tLTAbrdDIBDg/fffh8vlwtGjRzF9+nS/RtyGI1zAcZzmsiVMbzUO7nuB9s7Ozj5zkN6e6w9I41BCQgIWL1484p2iPB7P66zlyZMnIRAIEBMTA7lcPuri4XfccQfeeust6PV66t6empqK//3vfwgPD6ep26EqeVwsDIUwfal37Ny5E9988w0A3MMwzD3fP/UejuPOjOT6LxeQtB5JkzY2NkIqlWLChAmoqKjweRzJG2G6XC4qjCCTyTB16lSIxWIUFRX5dPMmIyQsy0Imk+HIkSP45ptvIJVKsXDhQvp84lBiNBqRmprar4H1nDlzcO+992LDhg0AfhhxcblcCA8Pp7U8dwQGBmLx4sU4dOgQRCIRrFarx3m6p0WJ0ANJ+QIX7kNbt26lJEoCAvfuW5Kd4vP5VEawoaEBERERyMzMxPjx4xETE4N//OMfCAwMxOrVqzF16lQsXrwYzzzzDKqrq8EwDHJycgbMdI0EYbrDXbRAIBB41dl1OByYO3cuKisrsXv3boSFhSEvL8/nYwxHuADApSdc4CvIl5NEXy6XC+Xl5QCA2bNnD/hB+xthsiyL0tJSSCQSWrwfTfSetSQ+f2VlZbDb7XRIPywsDGq1etgR6AcffIB33nkHsbGxWL9+PY4fP459+/ZBIpHg5ptvRmFhIebPn4+enh6oVCrU1NRALBbTCPhyEAsYCmH6Uu+44447cMcddwCA71ftjxjE37KpqQlhYWEeaVLS+OOLsYA7YRKln+bmZkRGRnpYgbk/diAhcpJ27OrqgkAgoFHNr371K/oY0q1LmpB8cShZu3Ytdu3aBZVKBYZhIBaLsWzZMvz9739HaWkpbrjhBnoePB4PTz75JG677TY8+OCDMJvNWL16NRoaGmhGh6Sie0envUFI1G63QywWIzw8vE8GRKvVoq6uDlKpFHl5eR4jH9dffz2uv/56D01tkurMzs4GALq5IM1CveujLpdrRDfOvjiVCIVCpKWlITs7G//4xz/8PsaPSrjAH7gPHNvtdhQXFyM6OhppaWmDfsn9iTDtdjuKiooQFxeHlJQUnD9/fkxlr4ALNZiUlBSkpKTA4XDQHSNJseTk5Ax5t7dr1y48+uijtBZTWFiI6upqPPDAAx6PgoIzBQAAIABJREFUYxjGw+PSZDJBpVLR5iVC4u4uBb5iLN7PK9ZeY4OKigqIRKI+pAb4T5h2ux2tra1oaWlBdHQ0ZsyY4ZUUB1L+cp+jDAoKwsSJE6kjSVNTE03zsSxLB/MzMzN9vpYYhsGePXuwYsUKNDc3Y/HixfjnP/8JiUSCefPmYceOHXj00UdhMplwxx134Oc//zlUKhXGjx+P8PBwHD9+HJ9++il0Oh0CAwNRXl4Op9MJrVaL3bt3D3if4vP5WLJkCa677jrccMMNHtdmXV0dOI7D+PHjB0xZugcW7ufsnmLub37UarUiICCgT2Q7VPjjhTlQ/Xu0hAsYhsm7bAmTXCQmkwlFRUXIysryWdvU1wiTvPb48eMRGxsL4MKXwmaz4dy5c2BZFqmpqWMaYQmFQsjlcuh0OkRERCA5ORmdnZ2oqakZkj3Y559/DpvNRqNUg8GA2tpa5ObmDvi8wMBAj+alzs5O1NfXQ6/XQyaTISYmBlFRUT53OV7xwvxxYPLkyf1ugHxV+2FZFjqdDj09PUhMTMTMmTMHdRHqTZjeBAdIMwupodpsNjQ1NaGnp4eWGQwGA4qLi8FxHAIDA2mjSnBwcL/mzunp6TTN1xvXXnstKisr0djYCL1eD7lc7pHilUgkJEPRB7fccgtV6BIKhcjMzERLSwtsNhuVsnvuuecwYcIE2hTU0NAAo9GI9PT0Yc20k+ux93VJunPr6+thtVqRkJBA3/vhCjH42hU9GGGOonBB/mVLmDwejzoiTJkypY+y/WDPHYwwNRoNzpw500dMgWVZfP7557QwHh0djfvvv3/MbsYcx9HU8/Tp0+kauO/twVQqFQoLC8EwDJ337L3DrK+vh06nw6RJk5CWlgahUEh3kU6nk24OfIVQKER8fDzi4+Phcrlo6vbcuXOQSCSUxPtTAfHWnj7SuEKYY4OBjBEGU/thWRatra1oa2tDcHCwz4IZ7oTpizIPURTq6enBuHHjkJmZ2ecx7mMQWq0WbW1tsFqtNJ1LSDQwMLDfqMjhcKCpqQnd3d1ISUlBVlaWX9mXDz/8EFu3bkVDQwOWLFmChQsXwmAw4P3334dWq8XChQvBMAyKi4thtVrhcrkQERGBpKQkBAQEjHijHsuy1Pw7NTUVUVFR9PV9FWIYaOzF19nKoerIAsMTLuA4rueyJUyLxQKNRoP8/Hy/I7zBUrKkTtfbTLqhoQHfffcdzp49i/z8fHAch9raWpw/f96vwvNQwbIsFWHoffExzA/2YJmZmdTdo7KyElarlaZM161bh82bN4PP5yMxMREHDx7E8ePHcerUKfD5fKxevRobN26ETCbDgw8+2KfoPhh4PB4iIyMRGRkJANTj8/Tp03C5XHQd7nOn3iS7Rhpms3nE3V2uwD/0F2E6nU60trZCoVAgPj4es2fPhlarRXd3t0+vS4h4MGUeu92O5uZmdHd3Izk5GRkZGf0SivsYhPsGkjiAGI1GKBQKGI1GsCxLFYKCgoIgkUigVqvR0dGBpKQkpKWlDen7LRQK+5RGgoODsXLlSgAXrhuFQgG9Xo+UlBTIZDIqNk8EA8ico3uk7K/pNOlKbmpqQlxcnFcrRPdGI3f0R6TumyryWTkcDp/WptVqfVLq8obhCBcAl2ENk/vezcRsNmPSpElDSocOlJJtbGxEe3s78vPzPT68o0ePYu/evVAqlaiurkZCQgLOnz+PhoYGmEwmPPPMM14l50YKTqcTRUVFiImJ8cmOzN3dg+irHjt2DK+//jot7tfV1eHtt9/G4cOHodVqUVNTg2uvvRZmsxlCoRDbt29HYWHhsNZNmivS09Nht9vR0dGB8+fPw2g00rnT/uyFRhJXIsyLj96E6XQ60dzcDKVSiYSEBA/tWF+0Z4Ef0vlKpRIulwvBwcF9FGQcDgeam5uhVquHRWDkHLxZaVksFhgMBigUCmi1WggEAohEIuh0OrAsS8lqJEbE3DuQo6KiMGPGDBrlBgUFeWwMSdnKaDTSuq3D4aAqPe4/3q5BrVaL2tpaqpTmL9l6I9LejUYcx1Gz6OTkZNoA5a3RiKxpqBHmcIQLgMuMMHt3qw4V3iJMd73Z2bNn9/mADx48iMTERISEhECj0WDv3r0ICAhAcnIyZDIZtm7dimeffbb3oUYENpsNhYWFSElJGdLOyl1fVSQSwW63U3eCyspKtLS0ICYmBv/5z39gMpnA5/NhsVhQUVGBJ598ckgzpt4QEBCAxMREJCYmUosulUqFzs5OOJ1Oug5f66/+4Aphjg0GSgEKBALYbDZKYB0dHUhMTPQqsj4YYbqnXonFnk6nQ1tbG2w2GwICAiCVSmGz2WA0GpGcnOyzSby/IOIfLS0tiI2NRW5uLm0kItEoUSIiTU/uaV2pVOrzujQaDerq6hAUFIQpU6YMeq3w+Xyv4xl2u71PpOxyuSCRSBAUFISAgADaVDhx4sRhOZD0hvu5chyHpqYmaDQaWncdTKheoVCMiua4L7hsCNNqtaKoqAhJSUlITk7G+fPnhyxm3jvCJEQslUqp3mxvkLqnSCRCZGQk7HY7MjMzkZaWRnUnR3ouCbiQei4oKMCECROGnVKcPHkyoqOj0draCpZlERgYiIcffhgOhwPFxcXQ6XTg8XhUqIDjOGzfvh3BwcG4+uqrR+iMLsDdokuv16Oqqop+xsCF4nxMTAyCg4NHpA5zhTAvPhiGQWdnJ1QqFZKSkpCfn98vUfRHmN5qlAEBAR4Nfw6HA42Njejo6EBISAjCwsLQ3t4OhUJB05Mk80HUY4YC90gvIiIC06dP94gg+Xy+R5MReQ4hcRL1mUwmqrXaO3VK1mY0GlFbWwsejzciBNbbK5OszWAwoLGxETqdDhKJBCzLorKy0uN9I4Q6nOvSPc2bmJiI9PT0fpuE3KPQ1157DUVFRaOyqfYFlwVh6vV6lJSUIDs7m3ogDsdE2j3CJGMj8fHxGDdunNfH83g8LFu2DJ988gmt/S1YsACHDx9GeXk5WJbF7NmzR3w+k3TsTZ48eUjK/L0hkUjw3Xff4e9//zu6u7tx7733YtasWQAudPqlpKTgyJEj6OjooDNlJG02muC+t1TKzMxEZmYmbDYbOjo6aOqdpG4jIiKGHCFYLJYrhDkG8HYNkG7Uzs5OCIXCAYmSoDdh+tLMQ2qhKpUKCQkJmDt3rsdxSCOPwWCgESGJRt1JlMjl9QeOu2Cw3tDQgJCQEJ8iPff3RywWQywW0zo/WRtJnbqvjcxlEseQ2NjYUSlfkHpoW1sbkpKSkJubS99f97Rud3c3mpubaWd977SuL2Mher0e58+fR1BQUJ9NRn/Yv38//vKXv+DOO+9EfX2936nhkcIlT5gdHR2orq7GtGnTPFRCBurGGwxETYOMjfgSvc2cORPJycnQ6XSIiYlBSEgIJk6ciKqqKkilUmRkZODYsWMIDQ1FbGwsoqOjhzXUS7p0p02b5nfjzUCIiIjodx4pPj4excXFyMvLo52rLMsiMjISJSUlI3Je3tC76UckEiEpKQlJSUlgWRbd3d1ob29HZWUllQyMjo7266K5EmGOPdxtu8aNG0fr/r5sesiGeChEOWvWLK/H6E/P1G63w2AwwGg0orm5GSaTiY6VuKdORSIRNBoN6uvrIRaLkZOTM2IjZTwejxI28EOHrVqtpiSp1WqhUCho6tR9bcNx/lCr1aivr0dERIRHPZSgv7Suw+Gg71t7eztMJhOcTidN65IfknK22+2oq6uDxWJBVlaWT6pPtbW1eOqppxAREYEvv/xyVLx4/cElTZgNDQ1QKpXIz8/vs4MjQsFDhdPpRGFhoV8jKSRNSJCfn4/8/Hz6O8dx0Gq1UCqVOH/+PIALu6m4uDhMnTrV5+ioq6sLZ8+e7VcLdzQRHx+P7du3Y8WKFbBarbjtttvwt7/9jXbe1dbW0hTYSKn8DNQly+fzvUoGkq5e4vYymJ7kFcIcGzAMQ6XldDod1V8mXZD+XLMsy8JgMEAsFnvM9bn/vbW1FUqlEvHx8Zg5c+aQoq+AgAAPUQ7AM+IjWrhGo5F2gctkMg+XkZGCy+VCa2sr2tvbkZSU5JX8iaYssdAizh9EsJwQaW9bst4gaV6BQIDc3Fy/r2WhUOg1rWu1Wj1qt2azGQ6HA06nE5GRkUhKSqKjbP2RvMlkwvr16/G///0P69evx/z58y8JLetLkjBdLhcqKyvhdDr7NOAQ+DJL2R+USiWsVisWLlw4ojdRhmFoB118fDwee+wxtLS0wGKxYMqUKXjiiScQHx8/4DHb29tRV1eH2bNnD9u9fCgwm80ICAhAaWmpxw2EnNeECRP6qPwM16LM15tOb8lAMjpz9uxZWCwWREVFISYmBjKZrM/rXSHMsYHT6UR5eTnGjRvXR1rOl85X94gyISEBtbW1sFgsHnJ2UqkUWq0WKpWKjjmMdJqSRHzECk8gEGDatGmQSCQwGAwwGAw0GgXQp8bnb42N1PSam5sRExMz4DmRemdgYKDHBt7pdFKi6ujoQF1dHZxOJ8RicR8SJRuAzMxMn8TwfQXDMJBIJJBIJIiKikJPTw9qa2tpVshsNtO5VmJ7RtZFhCGOHz+OV155Bffeey9OnDgxquYT/uKSI0yHw4HTp08jPDycmqV6w1BrmCRqDQwMHNUb6NGjR9HZ2Ynx48fD6XSiuLgYn376KRWM9kYyTU1NUCgUyM/PvyhfEqPRSGumA3Whuav89B4ViYyM9LveONRduvvoDHFjaGtrQ0VFBUJCQuhFKhQK/SZMX22AgAtZhNDQUAWA3RzHrfT7RH5EEAqFtC7eG4N5HPZOvZK0PHDhvqDT6aBQKNDT0wM+n4+AgADo9Xq0trZ6NPGMBNydStLS0jyiqP6iUYPBgO7ubiq5JxKJPEi0v9pod3c36uvrERoaiqlTpw75HAQCATWNJ3CP+EhDj9lshkgkQlhYGLRaLZxO54i+d8CF96+2thYcx3lEr73J2X2u9fjx43jhhRfQ09ODGTNm4LHHHhv1cTN/cUkRptlsRlFREdLT0wedafTXcYTjOJw9exY2mw2zZ8/Gt99+6/f6TCYT9Ho9wsPDafRns9lw6tQpaLVa5ObmUs9JMutotVqxf/9+mqpNT0/HRx99BJZlPUiGZVlYrdZ+I+rRBmkwmjp1ql87zt6jImq1GkqlktYb5XI5Ja3+MBJpLT6fT5WNOI6DTqeDSqVCfX09vvzyS5hMJvr++wJfbIAInnvuOQA4NqwT+BHB3XFjMPhSoyQuJW1tbYiNjUV2djYEAoFHE09voiIESojK18yH3W5HY2MjtFotUlNTERkZOehze9cfCUg3LFlf72iUeOmKRCJMmjRpVDbwpMlIr9ejs7MTsbGxdBPSez7Tbrd7NECR986f+5G7GlBGRkYfL+LeEAqFEAqFePvtt/Htt99i69atmDt3LlQq1SVHlsAlRJg9PT0oKyvzuSPUn6YfopATFBSEqVOnDiltWF9fj3feeQcOhwPBwcF4+OGHERUVhffffx9VVVUQi8U4duwYVeZITk5GeHg49u3bh+7ubvD5fOh0OjQ0NODgwYO45557kJCQQE11DQYDeDweysvLIZfLfdZh9QabzYann34aR48eRU5ODv7+978P+J7qdDqUlJQMu8Got0WZO2kJBAJKaL1vDCNdB2IYhu60x48fj7i4OOzduxePP/445s+fj9WrVw/6Gr7YAAHA6dOn0dHRAQCHcME/7woGASFTX4iyvb0dra2tiImJ6dOQ4t7EQ8ZK3Mc2DAYDraGRx7oTqftruYsbJCcne5XL8xcikQgikahPNNrd3Y3GxkbaoWs0GnHu3Lkhz2YOBJ1Oh9raWgQGBvaJXr018riPvLS0tNAGKKlU6pHW7d1k5G4jJpfLfZp5dblc2L17N9avX48VK1bgu+++o5/JxW7u6Q+XBGEqFArU1dX1kaIbCL5GmMTBOzExEcnJyUNe4/bt2xEYGIiQkBCoVCrs3bsXN998M2pqaqjyTktLCx555BHa2DB37lwEBgbCZDJBJBLR9mz3G0Z5eTmCgoIwc+ZMAPDQYQ0MDKTNNf6kaFevXo1t27bB5XKhvr4eKpUKBw4c8PpYjUaDsrIyzJgxwy8j1sHQm7QsFguUSiXOnDkDh8PhkZImYsijhfT0dIjFYuzbt8/n5/hiA0Qc6bdt24YdO3aM2HovdwwUYRLxArIZ7I8olUolWltbERUV5fPoAXk9b2MbRETAYDBAqVTCaDTSjk6WZWE2m5GQkIAZM2aMWmRD5kM1Gg3S0tKoCDvHcR6dur1nM92J1Ne0qdVqRV1dHex2+6COJe7oj+RJkxERh3DX1RUKhVCr1ZBKpT6P2FRXV2P16tVITEzE4cOHLxvZyotOmBaLBW1tbZgzZ45fpOBLDXOwsRF/xIlNJhN9DalUCoPBAJFIBD6fD6vVCrFYjPPnz0OpVCInJwculwvHjh1DWFgY7HY79Ho9nE4noqOjcf3114NlWRQXF0MmkyEjI4Meh9RHyBCxUqmkJtJyuRyxsbEQi8U4fPgwOjo6MG/evD4bgcOHD4PjONqJduLECa/n2t3djYqKCsycORNSqRSFhYU4ffo0MjMzsWjRIp/eF18hkUioGTVxN6mrq0NnZycCAwMhFApHRfhhIAzXBuiNN97AL37xCyQmJg7+4J84SOo1KCiI6iGHhIRQMiAbYJVKhZaWFup7OVK1/N4iAi6XC21tbWhtbUVoaChCQkJoI5FQKPSIRIOCgoYV7bl383rTsGUYhhKVt9lMg8HgkTYdSCnI6XTScZT09HSP1xsq+hvHMZvNqK2thVqtRlBQEKxWK0pKSjxGXshYCTlfg8GAV155BSdPnsSGDRswZ86cS6L71VdcdMKUSCT9NgkMhMFSsiTF219NjuzsfP2w5s+fjwMHDkAikcBqteLaa6+FRCLBbbfdho8++ggcx9EUB8Mw4PP5EAqF+O1vf4tt27ZRa5+tW7ciLCwMp06dQkJCQr9Rr7uYelZWFsxmM5RKJUpKSrB+/Xp8++23VOXk4MGDyMnJoc/NysqCQqGgO9fExETadZyTkwOBQEBHV2bNmgWJRIKdO3di5cqV1JNu1apVWLVqlU/vjb8QCoWIi4tDZ2cnxo0bh6ioKKhUKpw9e5aKXcfExIz6cPJwbYBOnjyJb7/9Fm+88QYA/A1AAMMwRo7j1ozaoi8D9E7VuadeMzMzPaI9hUIBg8EAu91Om09SUlIQHh4+Ko1vHMdBqVSipaUFUVFRmDVrVp+5QyIbZzAYPNKS7io8vkR75FjNzc00TenPhtBbbbR3ytk9GiUjPTExMX6JKfgLjuPQ3t6OlpYWJCcne4gckCYjEi0TEfi6ujp8/PHHOHfuHG655RYcP358xOe5xwLMIMX5sXVK9gMWiwXl5eVeyZbMQc6YMaPfFO/x48cxe/Zsnz80i8WCoqIiGAwGZGRkIDMzk/7NZDJR8WXipO5yuZCVlYXNmzfDZrNRwnQ4HCgsLERGRsaQ0pAqlQrZ2dl0rMZqteKaa67Bu+++i/DwcDAMA6VSiRtvvBFnz56FXC5HZmYmiouLwTAM8vLysGXLFjQ2NmL27Nn0opo6dSpaWloQEBAAlmXBMIzX6GskwHEcysrKEBAQ4DF64B5Vd3Z2gsfj0brncOZROY7DjBkzUFxc7PNzVq1ahYiICNr009PTg1dffbXfxzMMcy+A6Zd4l+yYXM9Op5POKBKJRW+pV47j0NHRgaamJoSHhyM6OppeR0ajEXa7nY5EkB+JRDKkiMS9xiaTyTBu3Di/NmTu0V5/6yPRFPBD52t4eDhSUlJGteudjG5IpVKEhobCYrHQ9fVugBpubVSr1eL8+fMICwtDamqqT/fPqqoqPPXUU4iOjsbs2bPR09ODtWvXDnkNYwSvX7LLj+K/R38RZn19PTo6OgZN8ZJBal8+8IaGBrz33nvgOA5yuRzz5s3z+DuZiYqMjMTbb7+Nr7/+GoGBgbjuuutoqiUkJISmiN0l/vwF2eDweDwqmxUQEICmpiaUlZVBJpNBLpfjxIkTcDqdOH78OH7zm9/QnW1RURHeffddPP300x43DIFAQF+b47hR2/31R5ZA36jaYrGgo6MDFRUVHhZlZGPgK8iNwx/4YgN0Bd5x6NAhyGQyZGVlISAgwOvgfWdnJ5qamhAWFuYRDfV2ASHRCtlIuc9kkpTuQFJ2HMehp6cH9fX1CA4ORl5e3pDmmweK9sj6VCoVJSoi7uFtJnikYDKZUFtbC4ZhkJOT0yc4cF+fu4gAwzAenbC+uKjYbDbU1tbCbrcjOzvbpw2sXq/HX/7yFxQXF2Pjxo2YOXPmZZV+9YbLNsJ0Op04efIkrrrqKgA/jI3Y7Xbk5eUN+iVtbW1FfX09dT7pLwWo1+tx++23w2AwQCKRICsrC9dccw1uuOEGv9arVqvxwQcfIDExEYsWLRqWNuwDDzyA3bt3w263g8/nY//+/Zg9e7aHA4harUZISAjKysrwzDPP0Jqv2WzGunXr8NBDD3m85uHDh3HnnXcCuLCbfuWVV3DfffcNeY3eQMyvBQIBJk6c6NfF43Q6qXC3TqdDeHg4YmNjfeom1mg0uPXWW3H48OHhnsJAuBzuBGNyPb/55ps4evQozp8/D4FAgEmTJiE3Nxc5OTlobm5GSkoKwsLCkJKSMqS0IZFkIz9kXKN3F6zJZKK6o2lpaaM6d202m6lQAGkCdI9GXS6XR6cpkdobCoE4HA40NDRAp9MhIyPDb+cO0nxI1mYwGOBwOCAWiz3eQ6lUCo7j0NLSApVKhbS0NJ/GbFwuF3bs2IHXXnsNjzzyCO6///5LckRkEHg9ycuWMDmOwzfffIP58+eDZVmcPn0awcHBVIbLVxBpqY6ODgiFQg8bLAD4+OOPsXHjRiQlJdHmnXvuuQd33313n9cinpVWq9WjdtrR0YEHHngALS0tEAgEiIiIwLZt24YcZdrtdsyfPx/V1dUQiURISUnB4cOH++x+dTodqqurceutt0Kr1YLjOISHh+O7776js1juqK2tRVlZGTIyMjB58uQhra0/DIcsvb0W6Sbu6uqCRCKhqVtvN2CFQoGHH34Ye/bsGc4pDIYrhNn7YN/rNZ85cwYHDx7Eli1bqIxhQkICJk+eTH9kMtmwvhPuJNDd3Y3u7m5wHIfQ0FCEh4dTEhgqSfUHu92OhoYG6PV6pKen97sRJnJ27kTvr/A7aVRSKBRITk6GXC4fsXPpHY0aDAbo9XrYbDbqsUki+oGi0crKSqxevRpZWVl4+eWXR6Tp6CLhx0WYwAU1nfz8/BEZGwFAh9tVKhUYhkFsbCz279+Po0ePQqfTISAgAJ2dndiyZQumTZtGn6fRaLBhwwbs3LkTFosF8fHxSEhIwFtvvQW73Y4vv/wSmzZtQmxsLBiGgUKhwB/+8Aca0Q3lvH/zm99AKBTSQv+aNWvQ3t4Oo9GI3/3ud5g+/YeRwJMnT+Lf//43xGIxrrrqKsTHxyM2NhZyuXxMtGo5jkNFRQV4PB6ys7NHxdVFpVKReUg6skI2EF999RVWr16N06dPj+hxe+EKYQ4AoslKNp5VVVUoKSlBaWkpysrKoNFoaAPJ5MmTkZeXh/j4eL/SmWazGfX19bDb7UhLS0NoaKiH5iohgICAAI+6qD/CBgTuA/rJycn02vYXZJyEEJXRaKQpU/e0qU6nQ319PaKjo5GcnDyqEZvZbEZNTQ0EAgFSU1Op5B5ZI4lGydpcLhcCAgKwbt06lJWVYePGjZgxY8aIr+u+++7DF198gejoaFRWVvb5O8dxePzxx7F//35IpVK89957mDp16lAP9+OqYQIXvrQnT57ExIkTvXYx+ovAwECkp6cjPT0dVqsVSqUSwcHBsNvt1Ix22bJlHmQJAJs2bcKpU6fol91kMqG9vR07duxATk4OpkyZ0ufCH05dw263ezRROJ1OrFu3jvpY/ve//8XBgweRm5uL2tpa8Pl8bNmyhV5kVqsVKpUKFRUVsNlslGBCQ0NHnMwIWTIMMypkCYDe+DIyMmCz2aBSqVBVVQWVSoWdO3fi9OnTAzbsXMHow30sISAgAHl5ecjLy6N/JzPDhES3bt0KhUKBqKgo5ObmUiLNyMjoU1+3Wq1oaGiAyWRCamqqxwyhN81V97pjV1eXV2GD4OBgr6TkLqZABN+Hcy17E353j5YVCgXUajWAC0IDRE1rOA1Q/cHpdNI50d6pXm+enuQ9XL9+Pfbv34/g4GCsWrVqVMgSAO655x6sXLkSd911l9e/f/nll6itrUVtbS0KCgrw8MMPo6CgYETXcNkSZk9PD8xmM+bNmzei4sEEYrEYKSkpSElJQW5uLo4fPw6GYTBhwgScO3cOcrmcjpDU1dXRVIxIJILBYKDDvLNnzwaPx8PcuXPx7bffgsfjQS6X47rrrhvy2n72s58hISEBjY2NVIXD4XDQGo3RaMT+/fupisj06dM9LmqxWIxx48Zh3LhxHjORBoMBkZGRI9aswHEcKisrwTAMJk2aNCYFf5FIRPVlm5qasGHDBmRmZuKFF17AkiVLLoqg/RUMDh6Ph4yMDGRkZGD58uUAfhAkLykpQUlJCfbt24e6ujpIpVLk5OQgNTUVdXV1WL58OdLT0/s0kfUHbzOP7lEUydS4XC4P4QC73U5nRP0RU/AXfD4fIpEIra2tsNvt1NrQvQFKpVLBbDZT8XL32q2/0ae7mTMRbxjofSTiEDU1NXjqqaeQnZ2Nc+fOQSKRQK/XD/f0+8W8efPQ1NTU798///xz3HXXXWAYBrNnz6ZypCMpinJZpmTb29tRW1sLlmWxcOHCMT22w+FAR0cHlEolTCYToqKisGfPHnz33Xdobm6GQqGg/pg7d+6kdUqn04mCggJYrVakpaVRKSxfzHS9wWAwYNeuXXA4HEhPT8ftt98OPp8PhmFgt9vx6KOP4oavMbELAAAgAElEQVQbbkBeXp7PROWuBdvT04PQ0FCqBTuUi7CyshIcxw0ooj9a0Gg0uO666/DSSy9h8eLFfs3cDhFXUrJjAFKb//DDD/Hyyy9j8uTJ6OzshMvlwoQJE5Cbm4u8vDzk5uYO2T2HgCjcqFQqtLe3A7jQTU4G84c76uIN7qne1NRUREVFDfjaTqezT0rXvcHIvXbrDe5mzmlpaT5tAjQaDf785z+jqqoKGzdu7JNxG000NTXh+uuv95qSvf7667FmzRr87Gc/AwAsWrQI69at8yhP+YEfR0rWfWzku+++G/PjC4VCJCQkICEhASzLorOzE/PmzUNHRwdtPpFIJFi8eHGfsY25c+eivb0dN954I3Q6HTiOwy9/+Uts2LABAFBTUwOn04kJEyYMSlDBwcG499576e/3338/3nrrLTAMg6ysLFx33XV+kSXQVwtWo9FAqVSipqYGUqmUNtb4MrB99uzZi0aWRqMRy5Ytw9NPP43FixcDGNgp4wouHxDJxRUrVmDFihUICAig4yeVlZUoKSnB7t27sXbtWpqida+LxsTE+PxdsFgsqK+vB8dxmDp1KoKCgmg6Uq/X94n03AnKX3Ug9yiPWJb58nyBQECt9wjcRek1Gg1aWlpgs9k83FPEYjHa29v9MnNmWRbbt2/Hpk2b8Ic//AFvvPHGqI3MDAXegr+Rvu4vmwiTRCwOh4OOjRw9evSSMRZ1OBx4//338c4770AsFoPjOGRmZuKNN97w2LW9+uqr2LJlC6KiouByuaDT6fDFF1/gX//6Fw4cOACGYTBjxgy8++67fivdFBQUYMeOHUhNTcVDDz00YrOUHMfBaDRCqVSio6ODppXlcnkf01mO41BVVQWn0+mhADJWsFqtWLp0Ke69917cfvvtY3noi/8lHByXzPU8FnA6nTh//jyti545cwYdHR2Ij4+nJDp58mSkpKR43PhtNhv1i0xPT/dpbKO/UReiPz3QvKNWq0VtbS2Cg4ORmpo6agpXhOjb2tqg1WohEAj6dOn2ZzpdWlqKp556Cnl5efjzn//s9yjLSGGgCPPBBx/EggUL6HWflZWFo0ePDjUle/lGmE6nEyUlJQgJCfGohRG1m4s94+NwOFBUVITW1lYkJCQgJiYGer0eJSUl2LJlC/Lz82lqU6fTwWQyUb1KhmFQUlKCAwcO0BTSqVOncODAASxdutTnNdTU1OCWW26B1WqFUChEcXExtm7dOiKExTAMvaAyMzOpkHppaSmcTidiYmIgl8sRFBSE6urqi0aWDocDy5cvxy233DLWZHkFlyDICNPEiRNxxx13ALgQfbW2tqK0tBQlJSXYuXMnFVDIysqCWq3GwoULce211/o1oiYUCiGTyTzGSlwul4drSn19PZxOJ02XBgQEoKurCxzHYeLEiaPesW4ymdDQ0ICIiAjk5ubS2WyyRnfTaYlEAqfTiTNnzuDEiRNob2/H66+/7tGoNdI4cOAAHn/8cbAsixUrVmDNGk+Fyffeew9PPPEELBYL8vLysHLlSqxYsYL+fenSpXj99ddx2223oaCggJaURhKXPGHabDYUFhYiOTm5z+wgEWy+mIRJ1peSkoLs7GwUFxdDr9fjm2++gdVqxa5duyCVSiGRSFBQUIAvvvgCWq0WGo0GIpEIv/jFL/Dtt99Cq9VCKpXSFJPRaPR5DS6XCy+99BI6OzvhdDppp+yzzz7rs/+jP3AXUicG0ufOnUNPTw9EIhFyc3NH/JiDgWVZ3HXXXZg/fz7uv//+MT/+FVwe4PF4tCnsV7/6FYAf0qGLFy/GhAkT8N1332Hr1q0QCATIzs6m0ShR0/GVRHk8Xh8LLY7joNfr0djYCJ1OB7FYDJfLRXsa3EUDRirdScycXS6Xh5kz0FeUnqzRZDJRFx6n0wkAmDBhwoisxxtYlsUjjzyCw4cP08ajpUuXYuLEifQxRGbU6XRCrVaDYRhs3rwZAPDQQw/hF7/4Bfbv34/09HRIpVJs3bp1xNd5SROm0WhEcXFxv2MjRB5vNHUaB4LFYkFBQQF1Q7nhhhtQWVmJTz75BDabDdOnT0d4eDg+/vhj/OY3v0FJSQlYlsXkyZOhVqthsVhQVVVFdSrPnTuH6OhoyGQyLFiwwKc1sCyLoqIidHR0wG63g8fjgWEYGAwG1NTUjAphuiMgIAAJCQkwGAzUUaWlpQXl5eUIDw+HXC5HZGTkqG5qOI7DQw89hKysLDzxxBOjdpwr+HGCYRjI5XKUl5fT7ykhjbKyMpSWluLDDz9ERUUF7HY7FfbwV3TB5XJBoVCgra0NSUlJmDx5Mn0eEVTX6/V+j7r0B3/NnMl5l5SU4KmnnsKMGTNw6NAhhIWF+XzMoaKwsBDp6elUJem2227D559/7kGYDz30EIqLi/H66697fQ2GYbBp06ZRXeclS5g9PT0oLy/HlClT+h0b8cXia7RgMBhQXFzsYXgtkUiwdu1a2Gw2lJWVITo6GizLUscGPp8PPp8PmUyG8PBw1NbWwmw2IzIyEuPHj4dCocDVV1+NP/3pTz4ZqDqdThQWFtImga+++or+TSwWj0lBnuM4nDt3DjabDVOmTKE3H47jqExfVVUVgoODqQvJSG5wOI7Dk08+iZCQELzwwgsj9rpX8NODOxkR8YC5c+di7ty59P8dDgcVXTh06BDWr18PjUaDpKSkAUUX1Go16uvrERER0ccIG/DuQ8myLK2Juo+6kJQuUd7pXfMkQvP19fV+NRCp1WqsXbsWDQ0N2Lx585hmihQKhYdNXkJCgtcZyk8//RTffPMNMjMzsXHjxjG31rskCbO9vZ0aSvduKnGHrybSIw2NRoMzZ85g2rRpCAoKwrfffov29nba1n7nnXeivLwcLS0t4DgON998M6RSKa677jp8+OGHaG9vB8dxmDZtGmpraxEaGkqdR6ZPn46WlhY4HI4BlXiI60lSUhISExNx880346233oLFYgEAyGSyobZT+4WamhpYLBZKlgQMwyAyMhKRkZE0DaVUKqm2p7u353Cwdu1aGI1GbNmy5ZJo/rqCHzeEQiGNLEmXusvlQkNDA20ueu+996BQKBAZGYmEhAQoFAr8v//3/+j9wlfw+Xxqwk7g3gHb3d1NPTKJ8o5QKERnZyckEgmmTp3qk1av0+nEe++9h7fffhtPPfUU3n777THvfvWlw/WGG27A7bffDpFIhM2bN+Puu+/G119/PVZLvLCmS6lLluM41NfXo6ury6fB4MbGRjQ3NyMmJgZxcXHDnrvyBZ2dnaiqqqKmy++++y4+/fRTaoC8evVqXHXVVWhqasLZs2cRGRmJmTNnQqVSobS0FEKhEHw+H1KpFNOmTcOzzz5LfRnnzZuH9evXg2VZOvtlt9upjB1pErLb7SgoKEBaWppHJHrs2DG89tprkEqlePbZZ0e15gAA586dg9ls7kOWg8FkMkGlUkGlUsHlctHz8+dmAgAbNmzA6dOnsW3btove+IUrXbIUq1atwt69e6noOfGA/SmB4zgcOXIETzzxBB07q6urg0QiQU5ODo1Gs7Ozh61vS3oe6urqYDQaIZFIqBPTQKMuHMehqKgIa9aswZw5c/DCCy+MigiMLzh58iRefPFFHDx4EADw17/+FQDwxz/+0evjWZaFTCaDTqcbrSVd2lqyREKN1Ph83eEQFwuFQgGTyYTo6GjExcWNisybe+QrEongcrlw8803Qy6Xg8/nQ6vVIjY2FuvXr/d4XlNTE+6//37U1NRAq9UiOTkZe/bsQUpKCjiOo4o9qampfdbscDigUqmgVCphNpsRERGBrq4uTJgwYcQ7wPxBTU0NjEYjpk6dOqz3mUjZEaPZ6OhoyOVyhIWFDfi6b731Fvbv349PPvnkotWwe+EKYX6PQ4cOYeHChRAIBHjqqacAAOvWrRuLQ19SIPdWd79XvV6P0tJS+kN6GEh2ikSvvm7+e5s5uwuyk1EXdx1YYt23e/dunD9/HgaDAW+88QYmTZo0em8EBu+ANZlMiImJQUREBKKjo2E0GrFr1y5kZ2fTx7ir9uzevRvr1q3DqVOnRmvJly5hOp1OnD59GmFhYcjMzBzyDZiQZ3t7OwwGAyXPwW6+vqCpqQkKhQIzZ86kN2iO4/Db3/4WYrEYgYGBUKlUyMnJwfPPP+/x3I0bN+L1119HV1cXAgICYLFYMG3aNBw9etSv1IfBYMCpU6cglUpht9sRFRVFZezGMh05UmTZG+TzUyqV0Ov1iIiIgFwuR0REhMf79OGHH+K9997Dnj17LiWpuyuE6QW7d+/Grl27sH379rE+9GUBjuNgt9tRUVFBU7rl5eUwGo2Dii4MxczZbrdj69at2LVrF4KDg2GxWPDuu+8iLS1t1M6RZVlkZmZ6dMB+9NFHHg09b7zxBr744gvU1dVBp9MhOjoaFRUVeP755zF9+nQsXboUf/zjH7Fnzx4IBALIZDK8+eabGD9+/Ggt+9IlTLVaDbPZ7NVyaqggKjzt7e3Q6/VDJk+O41BbWwutVotp06b1Sf0VFBTg1VdfBcdxCAoKwksvvdTnPP71r3/hpZdegt1uh1AopGnWkydP+jwAbDabUVhYiJycHERERIBlWajVarS3t0Oj0VByiYyMHNX6A9mVjjRZ9gaR6VOpVOju7kZISAi6u7uh0WjwxhtvYN++fX6ncEcZVwjTC2644QYsX76czkFegW9gWdar6EJcXBzS0tLQ0NCAhx56CPn5+T6p9HAch4KCAqxZswbz58/H888/79PzRgK+pFt//vOf48UXX0R+fj6cTidiY2PR1dV1MfsSLl3CHG2wLIuuri4oFAro9XpERUUhLi4O4eHhA34gROLN4XAMmCbu6emBWq1GXFyc15u4UqnE4sWL0djYCD6fT307jxw54hO5mUwmFBUVITc316vfHjGOViqV6O7uRmhoKOLi4nwyV/YHtbW10Ol0mDp16pg2BXAcB61Wi1WrVuG///0vZsyYgRdffBGzZs0aszX4gJ8UYS5evBgqlarP/7/88stYtmwZ/XdxcTE+++yzYd34PvnkE7z44ouorq5GYWHhmDSzXYpwuVwoKSnB8uXLMWfOHOh0OjQ3NyMkJITWRfPy8jB+/HiPztmOjg48//zz6OjowGuvveYR2Y0Fdu3ahQMHDuCdd94BAGzbtg0FBQUe4yGTJk3CgQMHkJCQAABIS0tDQUHBxfTTvHyVfoYLPp9PdVAJeTY1NaGsrAyRkZGIi4vrk9Z0uVwoLS2FWCweVJO1t8JHb8jlcurJWFpaiqysLLz66qs+kQ4ZX3E3pO4NHo+HqKgoREVFeWjAVldXIygoCHFxcYiOjh5Wre9ikSVwoQZUVVWFM2fOoLq6moo+jBRaW1tx1113QaVSgcfj4YEHHsDjjz8+Yq//YwRpVOsP77//Pr744gt89dVXw44SJk2ahM8++wwPPvjgsF7ncgePx8P06dOpVyXwg5k6US765z//iXPnzoHP5yM7OxsGgwG1tbV49tln8etf//qiaL/60gE7FjqwI4GfBGG6w508XS4Xurq66KB9REQE4uPjERISgtOnTyMiIgIZGRkjctzY2Fh88MEHfj1Hp9OhpKQE06ZN81ALGQgMw1ACnzhxIh3nqKurg1gspuMc/uhV1tXV0ZT0xbjgSkpKsHLlSuzdu5duDEYSAoEAGzZswNSpU2EwGDBt2jRcc801Y74T/7HgwIEDWLduHY4dO0Yt54aD0e72vtzgXqtkGAYRERFYvHgxNRrgOA5msxnl5eX4z3/+gw8++GBMjOL7Q0JCAlpbW+nvbW1tfebMyWMSEhLgdDqh0+kGDEIuFn4SKVlfQGpmbW1taG9vR3h4OLKyshAREXFRdjpk1nPGjBkjVqszGAxQKpVQqVRUlUculw/YOFNXVweNRnPRyLK6uhq33347PvvsM6oCMtpYtmwZVq5ciWuuucafp1162+G+GJPrOT09HTabjQ7hz549m0qYDQcLFizA3/72t59sSvZSR09PD5YvX46mpiaMGzcOO3fuRHh4OJxOJzIzM/HVV18hPj4eIpEIWVlZEIvFSEpKwp49e7Bp0yZUVFRg8+bN+Pjjj/HZZ59h586dF/N0fro1TF9htVpRUFCA9PR0CIVC2lAjk8kQFxfXp1tztNDd3Y2Kigo66zkaMJvNUCqVUCqVAEDJ0/149fX16O7u7mNAPVZoaGjATTfdhP/f3v0HVV3nexx/flHQjAhNgQPqUDk2hDZZIZh31dHNFH+BwjnuddJWm6nNdXRaM70299ruWHun1l1Hd2dy1bntjikH0UBDSxuzm5k/olqEDuIq8eNwOCdDXDF+HT73Dz3nIqIeOD++nOP78R96+H7f8M+Lz/f7+bzf77//fsBWexUVFUyYMIEzZ854vKq/TgLTC568E/U2MO90tEF4Z9WqVQwaNIjVq1fz+9//nvr6evdxosLCQlasWIHT6XQPxu64A7apqYnnnnuOr7/+mkGDBrFr166A/YF8CxKYt+PaWDNq1KgbXjS7NtRYrVYuXrzoDk9vd6M6HA7WrVvH2bNnmThxIq+++ir9+vXD4XBQUlJyxy5HvtTU1ORulODaoeaaQK9XWNbU1DBr1iy2bt3KE088EZB7XrlyhYkTJ7J27Vrmzp3b3W+XwPQzbwLTk6MNwjsdx2nV1tYyadIkysrKbvpcZGRkt4ZL6OTu3fRzJ653hWPGjLmpI0nnDTWu8CwpKWHgwIE9Ds+lS5dSUlLCfffdx44dO4iIiGDRokVYLBbS0tICer6wf//+JCYmkpiY6D4T5nA46N+/P2VlZQHrouTicDjIyMhg06ZNAQvL1tZW5s2bx4IFC3oSlqKX86S5t/BOXV2du7GAwWDAbrd3+TlXC9C+ffuyevVq99SYYNArAlMppduOKNfjT0/eFXbuj9oxPKOjo91HOe4Unq2trRQXFxMTE4OmaTidTj755BPGjRvHuHHj/DZA1hPV1dW0tbUxdepU2tvbqauro7y83N0IwmAw3PE4jjcuXbrE7NmzefPNN29oeu1PSimWLFlCUlKSTDvphfbu3cuyZctwOBzMmDGDxx9/3H2mz1OeNvcWt3e7R+eeqqysJD4+nvPnzzN58mRGjx7t18YJvtQrAvPzzz/nlVdeYfbs2ZhMJkaOHBmQ+9psNsrKynr0+LNzeP74449YrVZKS0vd5yBjYmK6DM/w8HASExOpqakhOjqaS5cu8eijj5KWlqZrm7cLFy64+/iGhYURFhZGQkICCQkJNx3HuVUXHm80NjYyZ84cXnvtte5uuPHKsWPH+Pvf/87o0aPdA3LffPNN0tPTA1aDuLXMzEwyMzO9uoY/ji0sXryY/fv3ExMTw5kzZ7y6VrC43XGi2NhYd/u62traLkcyAu4dsg899BCTJk3i66+/DprA7DXvMC9fvkxBQQE5OTnY7XYyMjIwGo1++0VWVlZSWVnJ2LFjfbqic52DtFqtOBwOoqKiSEhIuKmJwIULF1ixYgUWi4WkpCS2b9+u6zbqiooKbDYbKSkpd2x24NpR7GqU0PHRdE8bJTQ1NTFnzhwWLlzIggULenQNnQXDO8y7lqZp44B1Sqlnr3+9BkAp9ZYX15wAXAH+ppTybzNWHWmalg2sA5KAsUqp07f4XC4wCWgAyoFipdSqTp8ZCFxVSjVrmjYYOA7MUUqV+u8n8J1eE5gd1dfXk5+fj9lspr6+nrlz55KdnU1iYqJPrt9xIoon/Rd7qmMTAbvdTlRUlHvl2adPH86fP4/dbvcopPypO2HZmWt1XVtb6/4DwWAwEBMT4/HvtrW1lezsbKZPnx7Mh9MlMHsxTdP6AmeBKUANcAr4d6VUiZfXTQT2h3hgJgHtwLvAyq4CU9O0PsA5wArEAHHAVKXUcU3TngJeUkq9oGna09ev0w6EAX9SSm0L0I/itV4ZmB1dvHiRvXv3kpubS2NjI/PmzSMrK6tHg0OVUnz33Xfu+Y16tHezWq3ul+FhYWG6v7P8/vvvsVqtjB071uvQVkrR0NDg/hkHDBjgbpRwq0fNTqeThQsXMmbMGFauXOnV/XUmgdnLaZqWDvwJ6ANsV0p5/uLt1tdMJMQD00XTtE+5dWD6fAXfG/X6wOzI4XCQl5dHbm4ura2tZGVlkZWVdVPXiK4opfj2228JCwtj9OjRum0yUkphsVior6/n/vvvx263ExkZSUJCQrdWZb7gy7DsiqvLUF1dHeHh4cTHxxMXF+dua6eU4qWXXiIuLo433njD5/cPMAnMu5AEpvv/soBpSqkXrn/9HJCqlPp1YKv0r6AKzI5sNps7PDVNIzs7m3nz5hEbG3vTZ51OJ0VFRURFRXk1PsxbSilKS0tpaWlx96d1zcirqanBbrdz7733Eh8fT2xsrF/Ds7Ky0j2uLBCPgxsbG92NEsLCwjh9+jRnz54lIiKCDRs29Mq+kd0U9D+A6D5fB6amacOAv3HtkWY7sEUptdEX177DfQ9fv2dna5VS+dc/8ym3Dsxs4NlOgTlWKbXMf1UHXtAGZkc1NTXs3r2b3bt3069fP4xGI3PnzmXw4ME0Nzfz1VdfYTAYePDBB3Wr0TUgWynFY4891mVAuMLTarVSV1fHgAED3OHpy92zlZWVVFdXM3bs2ICuaF2uXr3K4sWL+eKLLxg2bBibN29mzJgxPru+TrsXJTDvQn4ITANgUEoVaZp2H/AVkNEbNsXII9kQCcyOKisryc3NZc+ePUREROBwONiyZQtPP/20bjW5HgeHh4fz6KOPejxJ/V//+hdWqxWbzcY999zjfqTpTXhWVVVRVVWlW1jCtYHaJ06cYMeOHdTX1xMREdHdNnS39dlnnxEZGcnChQslMIXfaJq2k2u7QgcDdcB/+XoDi6Zp+cBmpdQhX163h7V8yq0D0y+bqnqbkAtMF7vdzpQpU0hLS+PMmTMMGjQIo9FIRkbGLcdk+YNrTNi9997LI4880uNHj673gTabjf79+/coPKuqqqisrCQ1NVW3sNy6dSsFBQXk5eX59cxpRUUFM2fOlMAUQev66vUzYJRS6rKOdWQCm4AhwCXgG6XUs5qmxQNblVLp1z/n801VvU3IBmZbWxtnz551t74qLy8nNzeXDz74gLi4OEwmE7NmzfLpyqaz9vZ2Tp8+TXR0tE+bMXRcefbr188dnrfbbVtdXc3333+va1ju2rWLbdu2sW/fPr+3/pPAFMFM07RI4CiwXim1R+96xDUhG5i3Y7FYMJvNFBQUMHz4cEwmEzNnzvTpzDin08mpU6cYMmSIX7tYXLlyxR2erp2oBoPhhvDsDWG5b98+3n77bQoLC302rux2JDBFsNI0LRzYD3yklNqgdz3i/92VgdlRSUkJOTk57N+/nxEjRmA0GklPT/dqrFZbWxsnT54kPj7eZ80WPNHY2IjVaqW2ttYdnkopampqdA3LTz75hLVr13LgwAEGDhwYkHtKYIpgpF17Z/Me8KNSaoXe9Ygb3fWB6aKU4h//+Adms5nCwkKSkpIwGo1MmzatW48PW1tbOXnyJMOHD+9RcwVfaWxsxGKxYLPZuP/++xk6dCgGg8F9BjJQjh8/zrJlyygsLLxlb0l/kMAUwUjTtH8D/hco5tqxEoD/UEoV6leVcJHA7IJSiqKiIsxmMwcPHuSxxx7DZDLxzDPP3DZwWlpaOHHiBA8//LBHzRT8yWq1cv78eVJTU2ltbXWvPMPCwtyPbf39HvGbb77hl7/8JQUFBQH94+EXv/gFn376KT/88AOxsbG88cYbLFmyxN+3lcAUIsRJYN6BUopTp06Rk5PDoUOHePLJJzGZTEyZMuWGXZ7Nzc2cOHGCkSNHEhfX1fnfwOkYlp13ov7000/u8NQ0DYPBQHx8vM/D02KxMH/+fPLy8oJmEoGXJDCFCHESmN3Q3t7Ol19+SU5ODkeOHCE1NRWj0ciDDz7IF198wbRp0wL62LErtbW1nDt3zqNRYR3DE3CvPLs76qyzCxcukJmZyY4dO0hOTvbqWkFEAlOIECeB2UPt7e18/vnnbNu2jf379zN9+nSWLFnChAkTdJs80p2w7Oynn35yt65TSrlXnt0NT6vVysyZM/nrX//Kk08+2a3vDXISmEKEOAlMLy1atIgXX3yR5uZmcnJyOHbsGBMnTsRkMjF+/PiATUSx2WyUl5f7ZAh1U1MTtbW1WK1W2tvb3eF5p53DP/zwA+np6fzhD3/gZz/7mVc1BCEJTCFCnASml5RSN3TvaWtr48iRI+Tk5HDy5EkmT56MyWQiNTXVb+HpCsvU1FSfjwprbm52h6fT6cRgMGAwGG46s9rQ0MD06dNZt24dU6dO9WkNQUICU4gQJ4HpR62trRw+fBiz2UxRURHPPPMMRqORlJQUn03nqKuro6ysjLS0NL/P1ewYnm1tbRgMBoYMGUJ4eDgzZsxg+fLlZGZm+rWGXkwCU4gQJ4EZIM3NzXz88ceYzWaKi4uZNm0aRqORMWPG9Dg8AxmWnbW0tFBbW8vbb79Nfn4+48aN46233vL5jtiDBw+yfPlynE4nL7zwAqtXr/bp9X1IAlOIECeBqYOmpiYOHjxITk4OFouF9PR0TCZTtwZb2+12LBaLLmHp0tbWhtFoZPz48TzwwANcuXKFX//ad/NinU4nI0eO5NChQwwdOpSUlBR27tzp7g/cy0hgChHiJDB1dvXqVQoLC8nJyeH8+fPMnDkTk8l021BwhWVqamrAO/e4tLe3s2jRIkaPHs2qVav8co/jx4+zbt06PvroIwDeeuvaaL01a9b45X5eksAUIsQFZgunuKUBAwaQlZVFbm4uR48eJSkpiddff52UlBR+97vfUVZWdsPn7XY73333na5hqZRi6dKlJCYm+i0s4dpg8I4dgoYOHUpNTY3f7ieEELejTzdu0aXIyEjmz5/P/PnzuXz5Mvv27ePVV1/FZrORkZHB4MGDuXr1Kr/61c8usIoAAARvSURBVK90DcvXXnuNiIgIfvvb3/r9Xp35arOUEEJ0V0itMHNzc0lOTiYsLIzTp28aCh5UoqKiWLBgAQUFBXz88cc0NDTw+uuvk5eXx8aNG6moqNClrvXr13Px4kX++Mc/+j28hg4dSlVVlfvr6upq3Xv0CiHuXiEVmKNGjWLPnj1MmDBB71J8Kjo6mj59+lBcXEx+fj4PPPAAL774IuPHj2fDhg03hIo/bdy4keLiYrZs2RKQhgwpKSmUl5dz4cIFWlpa2LVrF7Nnz/b7fYUQoishueln0qRJvPPOOzz11FN6l+JXDoeDPXv2kJubS0tLC1lZWWRlZfllFbZ9+3b27t1LXl5eQHflFhYWsmLFCpxOJ4sXL2bt2rUBu3c3ybNiIUKcBGaIsNls7vAE3OEZGxvr9bXNZjNbtmxh3759XjdmD2ESmEKEuKDb9PPzn/8cm81207+vX7+eOXPm6FBR7xAXF8fLL7/Myy+/jNVqZffu3WRnZxMREUF2djZz585lyJAh3b7uhx9+yKZNmygsLJSwFELc1WSFGeKqqqrIzc0lLy+PyMhIjEYjmZmZDBo06I7fe+TIEdasWUNhYaFHn7/LyQpTiBAXUpt+xM2GDRvGK6+8wrFjx3j33Xe5ePEiM2bMID09nffee49Lly51+X1ffvklK1euJD8/X8JSCCEIsRXm3r17WbZsGQ6Hg+joaB5//HF3lxhxo3PnzmE2m8nPzyc2Nhaj0cjs2bOJiori22+/5fnnnyc/P5/hw4frXWqwkBWmECEupAJT9ExZWRlms5mCggKio6OpqKjgwIEDjBgxQu/SgokEphAhTgLTQ0E0NcMrR48epaGhQc47dp8EphAhTt5hesDpdLJ06VIOHDhAaWkpO3fupLS0VO+y/GLixIl+D8tQ6sgkhLh7SGB64OTJk4wYMYKHHnqIiIgI5s+fT35+vt5lBa1Q7cgkhAhtQXcOUw9dTc04ceKEjhUFt6SkJL1LEEKIbpMVpgdkaoYQQghZYXpApmZ0n3RkEkKEGglMD3ScmpGQkMCuXbt4//339S6rVzt8+LDeJQghhE9JYHqgb9++bN68mWeffdY9NSM5OVnvsoQQQgSQnMMUAReiHZnkpbYQIU42/fQiixcvJiYmhlGjRuldil9lZmZSXV1Nc3MzdXV1Pg3L4uJixo8f7/66qKiIyZMn++z6Qoi7lwRmL/L8889z8OBBvcsIasnJyfzzn//E6XQC8Jvf/IZ33nlH56qEEKFA3mH2IhMmTKCiokLvMoJaWFgYycnJlJSUUF5ezvDhw3niiSf0LksIEQIkMEXISUtL49ixY/zlL3+RFbsQwmfutOlHBJimaYnAfqVUaL/I9CNN02YB/wP8WSn1nzqXI4QIEfIOU4QiC9AM/LfehQghQocEpghFy4E1SqlGvQsRQoQOCcxeRNO0ncBx4BFN06o1TVuid03BRNO0hzVNswD3KKXe07seIURokXeYQgghhAdkhSmEEEJ4QAJTCCGE8MD/AQhV0z81CAMRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=plt.figaspect(0.5))\n",
    "ax1 = fig.add_subplot(1, 2, 1, projection='3d')\n",
    "ax1.set_aspect('equal')\n",
    "ax1.scatter(x, y, z, s=15, c='k')\n",
    "format3D(ax1)\n",
    "\n",
    "ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
    "ax2.set_aspect('equal')\n",
    "ax2.scatter(*projected_data.T, s=15, c='k')\n",
    "format3D(ax1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.765936Z",
     "start_time": "2018-12-27T18:11:36.763713Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.77381099, 0.22385721])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca2.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Principal Components from Covariance Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first compute the principal components using the square covariance matrix with the pairwise sample covariances for the features xi, xj, i, j = 1, ..., n as entries in row i and column j:\n",
    " \n",
    "$$cov_{i,j}=\\frac{\\sum_{k=1}^{N}(x_{ik}−\\bar{x_i})(x_{jk}−\\bar{x_j})}{N−1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `numpy`, we implement this as follows, where the pandas `DataFrame` data contains the 100 data points of the ellipse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.776792Z",
     "start_time": "2018-12-27T18:11:36.766830Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = np.cov(data.T) # each row represents a feature\n",
    "cov.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Eigendecomposition: Eigenvectors & Eigenvalues "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The Eigenvectors $w_i$ and Eigenvalues $\\lambda_i$ for a square matrix $M$ are defined as follows:\n",
    "$$M w_i = \\lambda_i w_i$$\n",
    "\n",
    "- This implies we can represent the matrix $M$ using Eigenvectors and Eigenvalues, where $W$ is a matrix that contains the Eigenvectors as column vectors, and $L$ is a matrix that contains the $\\lambda_i$ as diagonal entries (and 0s otherwise):\n",
    "$$M=WLW^{-1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we calculate the eigenvectors and eigenvalues of the covariance matrix.  The eigenvectors contain the principal components (where the sign is arbitrary):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.784540Z",
     "start_time": "2018-12-27T18:11:36.778247Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eigen_values, eigen_vectors = eig(cov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### eigenvectors = principal components "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.793345Z",
     "start_time": "2018-12-27T18:11:36.785848Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.71409739, -0.66929454, -0.20520656],\n",
       "       [-0.70000234, -0.68597301, -0.1985894 ],\n",
       "       [ 0.00785136, -0.28545725,  0.95835928]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the result with the result obtained from sklearn and find that they match in absolute terms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.802627Z",
     "start_time": "2018-12-27T18:11:36.794192Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.abs(C), np.abs(eigen_vectors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### eigenvalues = explained variance "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.817995Z",
     "start_time": "2018-12-27T18:11:36.803505Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.92923132, 0.55811089, 0.00581353])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.827485Z",
     "start_time": "2018-12-27T18:11:36.818910Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(explained_variance, eigen_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Check that Eigendecomposition works"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also verify the eigendecomposition, starting with the diagonal matrix L that contains the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.841270Z",
     "start_time": "2018-12-27T18:11:36.828502Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.92923132, 0.        , 0.        ],\n",
       "       [0.        , 0.55811089, 0.        ],\n",
       "       [0.        , 0.        , 0.00581353]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ev = np.zeros((3, 3))\n",
    "np.fill_diagonal(ev, eigen_values)\n",
    "ev # diagonal matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the result does indeed hold:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.850660Z",
     "start_time": "2018-12-27T18:11:36.842312Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decomposition = eigen_vectors.dot(ev).dot(inv(eigen_vectors))\n",
    "np.allclose(cov, decomposition)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Preferred: Singular Value Decomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll look at the alternative computation using the Singular Value Decomposition (SVD). This algorithm is slower when the number of observations is greater than the number of features (the typical case) but yields better numerical stability, especially when some of the features are strongly correlated (often the reason to use PCA in the first place).\n",
    "\n",
    "SVD generalizes the eigendecomposition that we just applied to the square and symmetric covariance matrix to the more general case of m x n rectangular matrices. It has the form shown at the center of the following figure. The diagonal values of Σ are the singular values, and the transpose of V* contains the principal components as column vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Requires centering your data! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we need to make sure our data is centered with mean zero (the computation of the covariance above took care of this):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.857667Z",
     "start_time": "2018-12-27T18:11:36.851546Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_features = data.shape[1]\n",
    "data_ = data - data.mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the decomposition does indeed reproduce the standardized data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.866451Z",
     "start_time": "2018-12-27T18:11:36.858486Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_manual = data_.T.dot(data_)/(len(data)-1)\n",
    "np.allclose(cov_manual, cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.875390Z",
     "start_time": "2018-12-27T18:11:36.867607Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 100), (3,), (3, 3))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U, s, Vt = svd(data_)\n",
    "U.shape, s.shape, Vt.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.886080Z",
     "start_time": "2018-12-27T18:11:36.876314Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert s from vector to diagonal matrix\n",
    "S = np.zeros_like(data_)\n",
    "S[:n_features, :n_features] = np.diag(s)\n",
    "S.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Show that the result indeed decomposes the original data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.896455Z",
     "start_time": "2018-12-27T18:11:36.889294Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(data_, U.dot(S).dot(Vt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Confirm that $V^T$ contains the principal components "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.902833Z",
     "start_time": "2018-12-27T18:11:36.897415Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.abs(C), np.abs(Vt.T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Visualize 2D Projection "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.911275Z",
     "start_time": "2018-12-27T18:11:36.903853Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "data_2D = pca.fit_transform(data)\n",
    "\n",
    "min_, max_ = data[:, :2].min(), data[:, :2].max()\n",
    "xs, ys = np.meshgrid(np.linspace(min_,max_, n_points), \n",
    "                     np.linspace(min_,max_, n_points))\n",
    "\n",
    "normal_vector = np.cross(pca.components_[0], pca.components_[1])\n",
    "d = -pca.mean_.dot(normal_vector)\n",
    "zs = (-normal_vector[0] * xs - normal_vector[1] * ys - d) * 1 / normal_vector[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:36.921338Z",
     "start_time": "2018-12-27T18:11:36.913308Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "C = pca.components_.T.copy()\n",
    "proj_matrix = C.dot(inv(C.T.dot(C))).dot(C.T)\n",
    "C[:,0] *= 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:49.253841Z",
     "start_time": "2018-12-27T18:11:48.522774Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TN2/eNNWF/yzMNpgTVfHrUK4hWzQaxdraGiYmJtSGbIFAAG6321DvYa7RNzazPR66uBgOiARi5JmDFy9eYG5uDnfu3IHP56vjmRmTkQaVdPzr0dzcjO7ubnR3dwP4LOBGo1E8e/ZMbcim9FjQoiHbeZjtTjvDDpExMRwQCUTvmoNyxy4UCpienkY6ncbIyAh3h3mFy4qMo5rXobW19cSGbE6nU61ZqHdDNjOGAzM9HoYDMguGAyKB6NnnoNzMwcHBAcLhMLq6unD79m1TXei1YIZwYIbHcFbHNWSLRCKvNWQLBAI17/ZttsG02XC3IjILhgMigei5lSlwdKC4sbGBhYUF3LlzB16vty7HFmlgJNK5XgRavB7FDdmuXr0KWZaxt7eHaDSKsbExtSGbsgxJ62J80T4DFw1fHzILhgMigejdIRn4bBnR1NQUstksRkZG6rJvvLJER7QL70W+624ktXodLBYLvF4vvF6v2pBtd3cX0WgUKysryOVy8Pv9aG9vh9/vP/eSOxE/A0QkHoYDIoHoPTAoFAr4v//7P/T29qK/v79u56P3jMlZ6P1a0VH1eD2sViv8fj/8fv9rDdkWFxchy/KRsGC3V3cJZjigepJlGYVCoer3KYmPrzgRVeT58+dIpVL4whe+ALfbXddjs7iXzkOv9065hmw7OzuIRCKYnZ2FzWZTw0IlDdkYDqie8vk8Pv74Yzx+/FjvU6E6YzggohPl83lMTk5CkiQ4HI66BwOA4YDOzwiD6oaGBnR0dKCjowMAkM1mEY1GK27IxnBA9cQC64uL4YCoSuvr67h8+fKF2LIukUhgdHQU/f396O3txf/7f/9Pl/NgOKDzMOp7p7GxEZcvX8bly5cBvN6Qrbm5Wd021e12MxxQXbHj88XFcEBUpZWVFXR0dJj6S1OWZaytrWFlZQV3796Fy+XS9XwYDvRhpoGoCI/luIZsS0tLSCQSaGpqQjabRSKR0L0hG5lfoVDgzMEFxXBAVCU9G5HVQy6Xw8TEBKxWK0ZGRgxRjMZwQOch6nuntCHby5cvMTc3h7m5ORwcHKgN2QKBAFpbWxkWdCTqe+wkXFZ0cel/1ScSjJnDQTwex+joKK5evYqenh69T0fFcEDnJfrA2WKxoLW1FU6nE/fu3TvSkG1qakptyKb0WKh1Q7bzMtsSKTMOpLms6OJiOCCqkhnDgSzLWFlZwdraGu7fvw+n06n3KR3BcEDnYZb3TvGAurQhmyRJiMfjakO2TCYDr9er1ixo3ZDtvCRJMl04MNtAmsuKLi6GA6IqGSEcaHnXLZfLYWxsDI2NjXj8+LEhLwYMB3ReZhiInjSgtlqtJzZky+fz8Pl8alioR/PCk5htMG22xwOYczaEKsNwQFQlvcOB0hBMi8HO7u4uxsfHce3aNbUI8jR6LAdgOKDzMMt7p5rP3nEN2SKRyJGGbIFAAD6fr+61RbIsm2owbcZwwGVFFxfDAVGVbDab7uHgvBciWZbx7NkzbGxs4MGDB3A4HBX9PWWQrkc40Hu2hsRmhpkD4OyPo1xDtlgshu3tbczOzsJqtaqzCl6vt+Z3jM22rMiMA2kuK7q4GA6IqqT3QPW8x89msxgbG0NzczNGRkaq+vLXIpicRa0HERsbG3j+/Ll6J9Xtdptq4HLRmWXmQMsBdUNDAzo7O9HZ2Qng84ZsL168wNTUFBoaGtTi5nIN2c6LMwfGJ+Kyop///Of48pe/rPdpCI/hgKhKRpg5OOtgZ2dnBxMTE7hx44baeKkaei3vqVUgKxQKmJ6eRiaTwc2bN7G7u6vuKe9wONRtItva2hgWBGeG16+Ws3bVNmQ773mYbebAjOFAxJmDv/iLv2A40ADDAVGVjFBzUO3xZVnG0tISNjc38e6776Ktre3Mx9YjHNTiuKlUCqFQCJcvX8bt27dhsVjgdDrVPeUPDg4QiUQwPT2NVCoFj8ej3kltbm7W9Fyotswyc1DPJX3lGrJFIhE1PLe1tanh2eFwVH1eZhtMm+3xAJ+Fg8bGRr1Poypm+azrjeGAqEqihYNsNotwOAyHw4GRkZFzXcD0XFKl5Zf+1tYWZmdn8fbbb8Pn8732cyUoOJ1ODAwMqNtERiIRhEIhdeeXQCAAv9+v+84vdDoz3KXWszdAa2sr+vr60NfXp4bnaDSK2dlZtSGbEp4racjGPgfGJ9pjMttslJ4YDoiqJFI4iMVimJiYwJtvvqmuLT7vsUWeOZAkCbOzs0gkEhgeHq74rljxNpE3btxAoVBALBZDJBLB/Pw8LBaLehfV5/OZ6g4i78QZh1EG1MXh+cqVK5BlGYlEAtFoVG3I5vF41GVI5Rqyme1Ou9keDyDesqLDw0O0trbqfRqmwHBAVCWr1YpCoaDb8StZ9y/LMhYWFrC9vY2HDx9q9oWpZ83BeY97eHiIUCiE9vZ2PHz48FyDLJvNhmAwiGAwCODzYs6NjQ1MTU2hqakJgUAAhULBMAO6i8wsr4FRH4fFYoHb7Ybb7X6tIdvo6Ciy2exrDdnMVpBs1t2KRHpMyWSS4UAjDAdEVdLr7nnx8U+aOchkMgiHw3C73RgeHtb0y12vZUXnDQfRaBSTk5O4deuWupWjlkqLOdPpNCKRCDKZDJ48eQKHw6FuI1nJkgvSlllmP4waDkqVNmQrFArY29tDJBJRG7K1traiUCggl8uZYlkeZw70l0qlGA40wnBAVCUjzBwcN0CPRCKYmprCW2+9hY6ODs2PrVcwOms4UGZQIpEIHj16VHZ5Qy20tLSgt7cXz549w/vvv4/9/f3XllwoYaGpqaku53TRiTCoPo0o4aCUzWZTG7IBQD6fx8rKCjY2NvCrX/1K94ZsWjBjOBCt5iCVSp15sw06SrxPIJHOrFYrcrmcrscvHSjLsoy5uTnEYrGaDoJFmjlQCrGdTieGhoZ0u3BbLBa4XC64XC61uFm5i7q6uop8Pg+/34/29nYWN9cIZw6MxW63w+VyqVsIFzdkm5mZgc1mq2tDNi2YMRyItqyIMwfaYTggqpLRCpIPDw8RDofh8/lqPggWpeZA6efwxhtvaFKIrSWr1Qqfzwefz4fBwUHk83ns7Oyoxc1Kp9pAIACv1yvUxdnIzDCoNks4AI42QSttyJbJZBCLxdQansbGRjUs1KIhmxbMGg5ECGYK1hxoh+GAqEpGCgfb29uYnp6u2Vr6k45dT5WGA1mWsby8jI2NjXP1c6gnu91etrh5fX0dk5OTanFzIBCAy+UyzeCwnjhzYDwnDaabmppeq+GJxWJYXV3F+Pg4Wlpa1ABtlM+EJEmmm/UTLRxw5kA7DAdEVTJCOCgUCnj69Cn29vYwNDRUt6ZcRp45yOVyGBsbQ2NjI4aHh4W6qBUrLW5Wmk8tLi6qnZuVsFDr8GOEQRd9zmzhoNLH0tLScqQhWzKZRDQaVT8TbW1tao+FszRk04Jo6/MrIdpsCGsOtMNwQFQlvcNBPp/H7Owsurq6MDQ0VNcLoVELkuPxOEZHR3Ht2jV1AGEWpc2n9vf31cLzVCoFr9erDoxY3Hw8MwyqzRQOzrOVaVtbG9ra2o5tyOZyudRlSPUaLIo2kK6EaDMHXFakHYYDoirpGQ62trbw/Plz9PX1YXBwsO7HN2JB8urqKlZWVnD//n04nc46n1l9FRc3K/vJl24Rqez64vf7hdz1pRa4rMh4tOpme1JDtsnJSaTT6VMbsmlBtOLdSon0fuOyIu3wykFUJT3CgSRJmJmZwf7+Pq5cuVK3LTlL6bmsqPQ5z+fzmJychCRJGBkZuZAD4ZOKm+fm5ljcXESkQc5xzNQ4rFaP5biGbJFI5EhDNiVAazXbZsaZA9GkUqm61N5dBBfvakrCy2azaGxs1O34NputruEglUohFAqhs7MTDx8+xMrKim4zF0ZZVnRwcIBQKKQutzHDwE8LpcXNmUzmSHFzc3Oz4Qo564EzB8aj1czBaYobst24cQOFQgG7u7uIRqN49uwZCoWCJlsJMxzojzMH2mE4IOH84he/wPvvv6/bRbKeS2s2NzcxOzuLO3fuwOfzAdB3WZMRlhVtbGxgYWEB77zzDjweT93PpVp6DuiamprQ1dWFrq4uAJ8XNy8sLGB/fx9Op/NI52YzM8Og2mzhQI/dfYp7KABQZ9ui0Sjm5+cBQP15NQ3ZGA70x5oD7TAckHCUu9d6XSTrMXOg7EaUSqUwMjJyZKbEarUin8/X9PjH0XNZUaFQUNcQj4yMCLFtoNEGcscVN09MTODw8FDt3Gy24mbOHBiPUR5L6WzbWRuyMRzojzMH2mE4IOEoW3nq9UVc6zv3yWQSoVAIXV1duHXr1msXUD1nDvQ6di6Xw8rKCgYGBso+J0ZmlEFQqXLFzcpyi+XlZRQKBbjdbmQyGeTzeeFrOoz4GlTLTDUHRh1MV9qQLRAIwO12q4/BqI/nrEQM1NzKVDtif9vThaT3VqK1PL6yZObOnTvwer1l/4xeS3uUY9f7ovHy5UssLy/j0qVLuHr1al2PfV4iDUitViv8fj/8fr9a3Ly5uYlIJIKPPvoINptNXYJk1C61xxFxoFOOWR4HYNzQXKpcQ7ZoNIqVlRXs7e2hpaUFgUAAmUxGqM/EaUTbxhTgsiItMRyQcOpdEFyqFuGgUChgamoK2Wz21CUzehUF1/vYkiRhdnYW8Xgc169fR6FQqMtxtaTXMiwt2O12tLe3w+Vy4eHDh2px89raGiYmJtDc3KyGBafTafiBntHPrxKiDKgrIeqd9paWFvT09KCnpwfA5w3ZDg4O8Ktf/epIjwW9GrJpQcSmblxWpB2GAxKOsqzILMff39/H6Ogoenp60N/ff+rF5CIUJB8eHiIcDsPv9+PRo0d48eIFUqlUzY9bC6KGg1Klxc3KoGh+ft7wxc1meQ24rMh4lIZs6+vrePDgAbLZLKLRKGZmZpBMJtWwYMTPxUlEnDngsiLtMByQcPSeOdDybvDz58+xtLSEu3fvwu12V3x8M4cDpXnRzZs31SJBUe/Ai3rXsBKlXWoTicSR4mav16sOivTcelhhhtfCTDMHZnoswOd32ss1ZFM+F0pDNqXov7m5We/TPpaITd04c6AdhgMSjt4zB1pc0EobeFWz847ey4pqtVOSLMtYWFhAJBLBo0ePjjR6EzUcAOa5a32S4sZT165dU4ubI5EIlpeXIUmS2rm5mu0htWKW18AsjwMwz8yBotzjKfe52NvbQzQaRTgcPtKQrb293RAhWiHqsiIjBy6RMByQcPSeOTivRCKB0dFR9Pf3o7e3t+qwYcZlRdlsFqOjo3A4HBgaGip7kRVxYGSmO6PVKC5uBj4Lw8XbQyr1DPUsbjbDa2GmZUVmmzmo5LUp7mhey4ZsWhBxWZGZPh96Yzgg4eg9c3BWsixjbW0Ny8vLuHfvHlwu15l+j95bmWo9SN/d3cX4+DgGBwdx6dKlsn9G1HAAmOtu71nZ7XZ0dHSgo6MDAI4UN4+Pj6O1tVUNC7UobjbLa2CmAbXZZg7O4riGbJFIBPPz87BYLGpYqPeMm4jLiszy2TAChgMSjt5bmZ5FPp/H+Pg4LBYLHj9+fK4vebPUHMiyjOXlZayvr+Pdd989sZBM1HDAi1V55YqbI5EI5ubmcHBwUJMiTjO8FmYKB7zL+7pyDdmi0Shevnx5pCFbIBCA1+ut6fMn4rIiEa8RRsVwQMIRbVlRPB7H6OgoBgYG0Nvbe+7fp3fNgRbHzuVyGB8fR0NDA0ZGRk69CIkcDkQ873pTipv7+/uPFHGOj48jk8mce122WV4DszwO4LPBp1mCTq00NDTg0qVL6oyqMuO2vr6OyclJNDY2qp+L4oZsWhBxWRFph+GAhCPKsiJZlrG6uorV1VXcv38fTqdTk98res1BIpFAOBzGtWvX0N3dXfFxRR0YiXreinqf/0nFzc+ePTtzcbMZBqJmuttupsdSL6UzbqUN2ZTleUp/kvO850VbVsRlatpiOCDhGGXm4KQpfuXOuN1ux+PHjzW9A6P3sqLzDBaVmotqw5Kej/k8zDAg1VtpcXMul0MsFlOXWuhR3KwXMy0r4szB+RU3ZJNlGalUCtFoFAsLC9jf34fD4VA/G21tbVU936LNHKTTaW5jqiGGAxKOEWYOlEEsWdzyAAAgAElEQVRyuS/bvb09jI2NVXVnvBoiLisqFAqYmJhQt26ttuaCMwekaGhoQGdnJzo7OwF81jAvGo1idXX12OJmswyqzfI4AM4caM1isbzWe+Tg4ACRSARPnz6tuiGbaDUHyWSS4UBDDAckHKvVilwup+s5KLMXxRe34gLbBw8ewOFw1OTYoi0rOjg4QDgcRm9vL/r6+s40uBF1QCTqeYukubkZ3d3d6O7uVu+elhY3Hx4eIp1Oa7a0Ty9mCgdmWgZixBsAFotFbcg2MDAAWZYRj8cRjUbVhmxKo8JyDdkKhULd+5GcBxugaUucV57oFZvNZoiZg+JBcjabxdjYGJqbmysqsD0PvcNBNRfCFy9eYH5+Hu+88w48Hs+5jivisiLAmAMHsyq+e6oUN8fjcXzyySeYnJw0dNOpSpgtHJjpsRg96FgsFng8Hng8ntcasoVCIeRyOfh8PjUsiLasKJVKnbjjHVWH4YCEY4StTIvrHnZ2dtR9+i9fvlzzY+s5UK50WZEkSZienkYqlaq6A/R5jms0Zhn8iEoZEDU3N+Phw4cAoBY3Ly0tQZZltbjZ7/cbfjBkpnBgpmVFoi3BAU5vyHZwcACfz6fW/OjZkK0SXFakLYYDEo4RCpKVuofFxUVsbm7ivffeq9tdCz3X31cSTNLpNEKhEDo7O3Hr1i3NBjOihgMRz9uMLBYLrFbrkaZT5YqblVkFIxY3mykccObAWEobsk1MTKC5uRmxWOxIQzZllzCjhSEuK9IWwwEJxwgFybIsY2xsDG63GyMjI3W9MOh5QT3tDv7Lly/x9OlTvP322+ruMvU4rpGJet6AeWY+jnsNKiluDgQCCAQCcDgcuj8fZgoHZnosZggHpWRZVjszA583ZNva2sLTp0/VXcLa29tr3pCtElxWpC2GAxKO3jMHsVgMsVgMb7zxBgYGBnQ7Dz0cN3MgyzJmZ2exu7uL4eFhNDU1aX5cEQfZZhn8mEElr0VpcbPSuXl2dlYtblbCQktLSx3O+igzDagB83w+ROsJUInSmoPTGrI1NTWpYcHj8dT9teXMgbYYDkg4es0cyLKMhYUFbG9vIxgMwuv11v0c9FbuDn4mk0EoFILP58PQ0FBNLgqihgNA7JkDszjLa2CxWOBwOOBwOHDlyhW1uDkSiWB0dBTZbPZIAWc9ipvNFg7MwowzB6fVURzXkG15eRnxeLzslsK1xJoDbTEckHD0KEjOZDIIh8NwuVwYHh7G1NTUhRz0lQ7SY7EYJiYmcPPmTQSDwbodVxQcyBnHeV+L4t1erl+/rhZwFhc3K4OhWq3JNtM6fTMxYziodjakXEO2SCSC+fl5tSGbUs9TbUO2SnBZkbYYDqgqqVQKjY2Nuu5/XO9lRdFoFJOTk3jrrbfQ0dEBwBh1D3pQlhXJsozFxUW8fPkSjx49qvkSC1HDAcCZA7MqLeAsXpM9PT2NhoYGdQmSlsssGA6Mx6zh4KwBt9yWwvv7+4hGo0casilhQYs7/qlUSr0+0/kxHFBVFhcX0dXVpWmxabXqNTCXZRlzc3OIxWKvDYCNsJ2qHpTn/pNPPkFbWxuGh4frclEUNRxwIHdxlK7JPjw8RCQSUZdZtLW1qTMLZy1u5rIiYzJjONBye1aLxQKXywWXy1W2Idvh4SE8Hs+xDdkqwWVF2mI4oKoYoQFZPWYODg8PEQ6H4fV6MTQ09NoX/0UNB4lEAvF4HPfu3atLTweFyOFAxPOm82tubj6yzEIpbp6ZmUEymYTb7VbvnFY688ZwYExmDAe1LLI+riFbJBLB6urqaw3ZKqnnYUGythgOqCpGCAe1njnY3t7G9PT0ievoL1o4kGUZKysrWFtbQ1tbW12DASD2IFvU8ybtlCtuVrrTFhc3K2HhuIZTrDkwJhGboJ2mnk3qihuyDQ4OHqnnefbsGSRJUj8fPp+v7OeDNQfaYjigqui9jShQu4GiJEmYm5vD7u4uhoaGTpzaNEI4qNddxHw+j/HxcdhsNoyMjOCjjz6q+TFLiRoOOJCjciwWC7xeL7xer1rcvLOzg0gkgsXFRQAo23CKMwfGZMaZAz2V1vPk83nEYjFEo1HMzc3BYrGgvb0d8Xgct27dgsPhqGrm4Lvf/S5+8pOfIBgMYmpq6rWfP3nyBF/96ldx5coVAMDXv/51/NVf/ZV2D1AADAdUFSMU4tbi4phOpxEOh9He3l7Rdpx6hwNlS9FaDxQSiQRGR0cxMDCAnp4eAPrcCRc1HACcOaDT2Ww2tXgZ+Ly4eXNzE9PT02hsbEQgEEA+n9f5TKkcM/Y5MBK73Y6Ojg614DibzSIWi+Gf/umf8NOf/hQOhwNOpxOzs7O4devWqcuQvvOd7+CDDz7At771rWP/zG/8xm/gJz/5iaaPQyQMB1QVIywr0prS1ff27dvqnYrTGCEc1Ppu1fPnz7G0tIR79+7B5XLV7DiVOK75mtHxLi+dRWlxs7KHfDabxZMnT9DW1qaGiVpsC1lrZgvMnDmor8bGRly6dAk/+MEP8IMf/ACrq6v4wz/8Q/zXf/0X/uZv/gadnZ34zd/8TXzpS1/C3bt3X1vy9YUvfAErKyv6nLwgGA6oKjabDZlMRu/T0IQkSZiZmcH+/n7VXX2tVityuVwNz+7049dqsFwoFDA5OYl8Po/Hjx/rum2tgjMH+hH9/M1A2UN+aWkJ77//Pg4ODhCJRNRtIZXi5kAgcKadXurNbINpsz0e0fT19cFut+Pv/u7v4Pf7sba2hv/5n//B3//932N0dBQ//OEP8YUvfKGq3/nLX/4Sd+7cweXLl/G3f/u3uHnzZo3O3pj0v+qTUMwyc5BKpRAOh9HR0YGHDx9WfedN75BUq3CQTCYRCoXQ09OD/v5+w9yRNMp5VEvU8ybjslgscDqdcDqd6raQyk4v4XC44uJmPdWz2LUeJEky5PN8ViLeECjeyrS3txff/va38e1vfxuyLFd9rbx37x5WV1fhcDjw4Ycf4mtf+xoWFhZqcdqGxXBAVTFCQfJ5bW5uYnZ2Fnfu3IHP5zvT79B7mUst7qRvbm5ibm4Od+7cgdfr1fR3X1Qiz3iQGIqLm2/cuHGkuHlhYUEt3mxvb69Z5+ZqmW3XJbPNHIj4eA4PD8vOmlkslqrf88XLaL/yla/gT/7kTxCNRitedmwGDAdUFSMUJCuqLcgtFAp4+vQpUqkURkZGKto7+Th6hyQtZw4kSVKXJwwPD5/reaHXMRxQPZUWN2ez2bLFzYFAAG63W5dBuhlnDsz2eIwQIqul1Xt5a2sLHR0dsFgs+OSTTyBJkq6NX/XAcEBVMcqyImVwXOkXWDKZRDgcxuXLl3Hr1q1zf4kYpSD5vNLpNEKhEDo6OnDz5k1T3c2rRjKZxNjYGKxWKwKBAILBIJxO57mfj4v6fJJxNDY24vLly2pvknQ6jUgkgqWlJSQSCV2Km804cyDiYPo4hULBVI+n1De/+U08efIE0WgU3d3d+P73v6/WEH7ve9/Dv//7v+Mf//EfYbfb0dLSgn/7t38z1fu1EgwHVBWjhAPlzn0lX2AbGxtYWFjQdLmM3uFAi2VNSrO3anZpMiNlt6p33nkHTU1NiEQimJ+fx/7+PlwulxoWzlLoyWVFZDQtLS3o7e1Fb28vZFlWi5unp6eRSqXg8XjQ3t5e0+JmzhwYm9m3Zv3xj3984s8/+OADfPDBB3U6G2NiOKCq6L2cRqEsbzqpCKxQKGBqagrZbBYjIyOaFozpHQ6UPgdnIcsy5ubmsLOzc2qzNzMrfh6Kd6vq6+tDX18fZFlGPB4/Uujp9/sRDAbh9/sNsYsT0XmUFjdLkqS+50OhEHK5nNqMze/3a/YdysG0sZl95oBOx6sbVcVoMwfHOTg4QDgcrtmuO3rXXpw1nGQyGYTDYXg8noqavZlVNptFOByG2+0+9nmwWCzweDzweDy4fv068vm8Wug5OzsLu92O9vZ2BINBeDyeY59LkWcOLur746KyWq2vFTfHYjF1Nk0pbg4EAvB6vWceQJpxWZGZwoFoy6TMFs6MgOGAqqL3oLiS81Cad73zzjvweDw1O76eg76zhINYLIaJiQm89dZbaqfJi2hvbw9jY2MYHBxUm0xVwm63IxgMIhgMAvhsd4xoNIrl5WXE43G0tbUhGAyqa7cBDq5JbDab7ch7Xilu3tjYwNTUFJqamtSwUE1xM5cVGZtog+1UKqVuY0raYDigqhhl5qDc4Difz2NychKFQkHzZUTljq/n81BNzYEsy1haWsLW1hYePXqElpaWcx+/2p2ijGJtbQ3Ly8t48OABHA7HuX5Xc3Mzuru70d3dra7d3t7exuTkJNLpNHw+HzKZDNxut0ZnT6Sv04qbHQ6H2l/hpOJmzhwYm2jLihgOtMdwQFUxSs1B6XkkEgmMjo6iv78fvb29Nb/wiFJzkMvlEA6H0draiuHhYU0uYMqxRbq4K/Un+XweIyMjmtcLFK/dvnr1KiRJwu7uLp4+fYrZ2Vk8e/ZMvcPq8/lMNZCgi6u0uHl/fx/RaPRIcbMSFoprm8w4cyDSYPo0IoYDZbaWtMFwQFUxyu4ryp17WZbVu8H37t070ryk1sfXOxycdnxl+cyNGzfUO31aUGYtRLm4p1IphEIhdHV14cqVK3UJNVarVS3k9Hg88Pv9iEQi6nKM5uZmdftILbZMJdKbxWKBy+WCy+VSi5uVzs2rq6vI5/Nq52blz5uFSN+HlRDt8RR3RyZtMByQkGw2m3pX3GKx4PHjx3XdPUbvcHDSsiJZlrG6uoq1tTVNls+U0rveohrKdq3n6YZ9HkqYbmhoOLIcI5VKYXt7G3Nzczg4OIDb7VbDwkXdPYrMxWq1wufzwefzYXBw8EhB/9bWFvL5PBoaGtTOzSINRkuJtkb/NCLOHDAcaIvhgISUzWYxNTWFwcFB9Pb21v34eoeD4wbo+Xwe4+PjsNlsGBkZqckXvFFmj04iyzIWFhYQiUQMuV1ra2sr+vv70d/fD1mW1TusoVAI+Xz+yPaR3DKVALF3vQKOFvS3t7dje3sbLpfrSHGzEpBdLpdQMwtmWyYlYjjgsiJt8apDQlHuir98+RJXr17VJRgAxggHpcff399HOBzGlStXavq8aNGArZaUGSWHw4GhoSHdL9qnDeosFsuR7SPz+by6faSyZaoyaDppy1QyN9HqfE4iSVLZ2bRIJILFxUXE43E4nc4jnZuNzGwzB5IkobGxUe/TqBhnDrTHcEDCyOVyGB8fh91ux8DAgK5fXnpfpEvDwfr6OhYXF+tSd6HnsqLTBkiJRALhcFjzOouzOsv7xG63o6OjQ91u9vDwEJFIRN0yVdkRJhgM8oJ4gZgpHJR7LK2trUcaEO7v7yMSiWBqagqpVAper1ct6lcaFhqFmV4bQLyww5oD7TEc0JnU+8tQKa69du0auru7sby8bOi717VmsVhQKBTUXXhyuVzNt28tPrYez72ynOm4993z58/x7Nkz3L9/H06ns85nV54WS7Cam5vR09ODnp6eI4OmiYkJHB4ewuv1qndY6/H6kz7MNAA9reC1uLhZ2f2rtLjZaEvvzPLaAGIuK2I40Jb+nygSjtLroB5fyLIsY3l5Gevr60eKa202G/L5fM2Pb1RWqxWpVAofffQRuru767YLj3JsPWYOjhtoS5KEqakpZDKZmmxTel5aPlflBk1Kkefi4qLawTYYDMLr9Qp1949OZqZ17dU+lpOKm+fm5mC1Wo90bjbL86QX0bZmZc2B9ox1FaVj5XI5zMzM4O2339b7VOoWDrLZLMbGxtDU1PRaca3eTcj0lkgksL6+jvfeew9er7eux9Zr5qBcKEmn0wiFQrh06RJu375tuLt39ei30d7ejvb2drz55ptqB9vnz59jYmICLS0t6hIkh8NhuOeHKid6QXKx8zZBK+1WnslkEI1Gsb6+jsnJSaGLm41AtJmDZDJpiGWkZsJwIAiLxYJ4PK73aQCoT5fknZ0djI+PY3BwsOyH3ijN2OpNkiTMzMwgEomgp6en7sEA0G+3otLjRqNRTE5O4vbt22hvb6/7+VSi3s9VaQfbZDKJSCSCmZkZJJNJuN1uBIPBqtZtm2lQKrKLtKyoWk1NTejq6kJXVxeAz4ubFxYWsL+/D6fTqc4s8A7z6USrOeCyIu0xHAiiHgPyStXyXGRZxtLSEjY3N/Hee+8d+0V+EWcO0uk0wuEwAoEABgcHdQuLei8rUt4jW1tbePToEVpaWup+LqJoa2tDW1vbkS1Tt7e31XXbyoDJ7/cLdafwIrrIy4qqdVxx8+TkJNLptFqn097ebrjiZiPgsiJiOBCEke4Y1Wobz2w2i3A4jLa2NoyMjJx48dB7K9F6U5p5KXfJt7e3dXv8ehYkKztWNTc3Y3h4WIjBklHuvBdvmaqs247FYnj58iWePn2KxsZGdSmG2+021HcOmW/moF7F8+XqdHZ3dxGNRrG8vIxCoWC44ma9ibasiDMH2uOngKpWi5mDWCyGiYkJvPHGG7h06VJF56B3ODht9xwtyLKM+fl5RKPRI8289AxHei0rKhQK+OSTT3D9+nV0d3fX/fhnYeSGcaVbpqbTaUQiESwtLSEej8PlcsHr9V64GTqjMur76Cz0nAWxWq3w+/3w+/1HQrLSV8Rms1VV3Gym10Uh2rIibmWqPYYDqpqW4UDpZLu9vY2HDx9W/AE3wrIi5Rxqdacpk8kgHA7D7Xa/1sxLz0Zkeiwr2tjYQDwex3vvvYdAIFDXY5+HSHd6W1pa0Nvbi97eXsiyjEQigc3NTezv7+PJkyfw+XzqUgxumVp/ZlpWdN6CZC2VhmSluLm0qL+9vb1scbPW9RNGwGVFxHBAVdMqHCiDX5fLVfUSESPMHNRykKwUZL/11lvqRatexz5NPYOJJEl4+vQpUqkU/H6/kBcAEe8sWiwWuN1uNDc3Y2dnBw8fPlS3jlxYWIDFYlGXIHHryPow07IiIwed0uLmZDKJaDSKhYUFJBIJuFwu9b3f2tpqynDAZUXEcCAYI1wgtFjSouw0c9zgt5JzMMrMgZZ3UWVZxrNnz/DixYsTZ1L0XFZUr2ByeHiIUCiEYDCImzdv4tNPPxVuoK33Z1UrNptNHRABn9UHRSIR9e5qa2ur+nOjbZkq2nvmOEb47teKkWYOTqMU9SvFzYlEQm1CmE6n4XK5kMvlkMlkTFPcLNLrA3BZUS0wHAjEbrfXrfnYSc4zcyDLMubm5hCLxc6104wRCpK1PodcLofR0VE0NzefWpCt57KiehxbqUG5deuWOiA18vr94+j5OmnhuAFCY2OjendVlmV1y1Rllsfj8ahhwQgDJpEGOscxUzgw8szBSZQZNbfbjWvXrkGSJGxtbWFvbw+//vWvUSgU1L4johc3i/Re48yB9sR9515A9exMXMl5VOvw8BDhcBher/e1NfT1OgctaRkO4vE4RkdHcf36dXU6+7Rj67msqFbHLp45KQ2Pog60RQs01bJYLHA4HHA4HLhy5QokScLe3h4ikQhWVlbUAZNeW6aa5fk3UzgQ7c70caxWK9xuN1wuF959992yxc1KSPZ4PEIGIhGYadbGKBgOBGKEAbFyHrlcrqq/o2zFefPmTbWr5XmYZeZAlmWsra1hZWUFDx48gMPhqNuxz6pWwSSfz2NsbAwNDQ0YHh5+bRBphsHERWC1WuHz+eDz+TA4OIhcLodYLIatra0jW6YGg8G6da81w3vHbOHALAPl4p19jituXltbw/j4uFrcHAgE4HQ6TfN6GgGfS20xHAjEZrMhn8/rfRqw2Ww4PDys6M9KkoS5uTns7u4e2YpTi3MQPRzk83lMTEzAYrFgZGSkqhkhvbcy1frYBwcHCIVCGBgYQE9Pz7HHFe0usIjnrLWGhgZ0dnais7MTwOdbpi4uLiKRSMDpdKphoRYN7czy/JspHIi6rKick4JOueLmSCSCubk57O/vw+12q7NqXBZDRsJwIBCjzBxUOjBVOvq2t7djaGhI0wubEQZd5xmg7+/vIxwOo7+/H319fVX/fb1rDrR87l+8eIH5+XncvXsXbrf7xOPqHQirZZbBnJbKbZm6vb2N0dFRZLNZ+Hw+BINB+P1+zYr9zfA6mCkcmGVZEVDdLEhpx3KluHl8fByHh4dHtgtubGys8ZkTHY/hQCBGCQeVnIfSdVXp6GtGZw0H6+vrWFxcPHUwfNqx9QpHWh1bkiTMzMzg4OAAw8PDp14MjRAIz0LEc66X4gLP69evo1AoqGu25+fnYbVaz71m2yzPv5nCwUWZOThJueLm3d1dRCIRPHv27Eitjs/nq1utoZmCG50dw4FARAgHyoAvkUhgeHjY1EVC1YaDQqGAqakpZLNZjIyMnOuuqOjLijKZDEKhEPx+P957772KLkYihgNeZKtjs9kQDAbVuqRMJoNIJILV1VWMj4+jtbUVwWAQgUAAbW1tFT+/ZngdzBQOzDQA1ap+orhzMwC1Vufly5eYmZmB3W5Xw0Iti5tF63GQz+eFOl9RMBwIxOjhIJVKIRwOo6OjA48ePTLNl/9xqql7SKVSCIVCuHz5MgYGBs793OhdkHye2helwVu1xel6zpaclYiBxkiamprQ3d2N7u5uyLKMg4MDRCIRTE9PI5VKwev1qjMLx808meX5N1s4uOgzB6cprdU5PDxENBo9EpSVsKBlcbOI3ZFZr6E9hgOBKH0O9FZuYLq5uYnZ2VncuXMHPp9PpzOrr0oH6FtbW5iZmdH0udFz0HnWmQNZlrGysoL19fUTG7yddFwRB3oinrMRWSwWOJ1OOJ1ODAwMvLYMQ5blI8swigc4ZhhUmykcmOmx1CvoNDc3HwnKqVSqJsXNxbsviSCVSqGtrU3v0zAdhgOBGHHmQJIk9S7eyMjIhSqiOi0cKEus9vf3TfXcnOUOvrIzk9VqLbtNaSVEDAdmGQAZUfEyjDfeeAO5XA7RaBSbm5uYnp5GU1MTAoEAvF6vcO+bcjigNiY97rRbLJbXipvj8Tii0SjGx8eRyWTUWbVqi5tFW1bEmYPaYDgQiM1mQzab1fs01HCQTCYRDodx+fJl3Lp1q+4XLmWwqNcF02q1HhvWDg8PEQqF0N7ejocPH5rmog5UP3OQTCYRCoXQ19d3pp2Zio8r4iBPxHMWUUNDAy5duoRLly4BgHpndWlpCXt7ewiFQuoSpFpsmVprZgoHZipINsKddovFAo/HA4/Hg2vXrqFQKKizaktLS5BlGX6/v6JGhKKFg2QyyXBQAwwHAjFSn4NUKoVf//rXuHPnDrxery7noQzO9eoYfdwd9EgkgqmpKdy6dQuBQECHM6utagbpW1tbmJ2dxTvvvAOPx1O34xqFGQZzoj3nitbWVvT19aGzsxOffvoprl69ikgkom6ZqgyW2tvbde86XwmzFfGa6bHoHQ5K2Ww2tLe3qzsFFhc3P336FA0NDccWN4tYc8BlRdoz/jciqYywrKhQKGB6ehqZTAZf/vKXNduH/Cz07pJstVqPdIqWZRnz8/OIRqOaNnwzmkqWFcmyjNnZWezt7VW0TWklRAwHgLiDazOxWq3qndXSLVPn5ubUnWCCwSA8Ho9hB65GPa9qmWnmQJIkXa+DlaikuFkJyvl8XqjXhsuKaoPhQCB6FyQfHBwgHA6ju7sbu7u7un8h6h2WisNJNptFOByGy+XC0NCQUF+u1TptWVE2m0UoFILX69V01yoRw4FZBnMiK/eeKd0yVRksLS8vIx6Po62t7ciWqUZgpmVFnDnQV2lxs9K5WbmhY7fbsba2JsQSPC4rqg2GA4HoORhWGncpy0PW1tZ0OY9iRpg5kCRJ3ZrzzTffVO/MmNlJg/S9vT2MjY3hjTfe0Py5EDUciHbOZnTaQLR0sHRwcIDt7W1MTk4inU4bonOtmQbUgHmCs4jhoJjFYoHD4YDD4cCVK1ewsbGBaDSKTCajLsE7a3FzPXDmoDYYDgSiRzjI5/OYnJxEoVA4d+MurVXTZ6AWLBYLYrEYtre3z7Q1p6iOC2Wrq6tYXV3Fu+++W5O7raIOtEU8ZzOp9vkv3jL16tWr6pap29vbWFpaAoAjW6bWa2BoppkDMxFtjf5pJEmCw+HA1atX1SV4pcXNSj3DacXN9cCag9pgOBBIvQuSE4kERkdH1V1mjHZhOmm3oFrL5XJYXFxEoVDAb/zGb+j+BVlPpYP0QqGAiYkJyLKM4eHhmhV3ihgOjPaZuajO8zqU61wbiUSwsbGBqakpNDU1qUuQtGxGVYrhwJjMNqNTuvtSueLmaDR6pLhZ2QVMj3odzhzUBsOBQOo5c7C2toZnz57h3r17cLlcdTlmtfSaOYjH4xgdHUVHR4eurdv12sq1uCA5lUrh008/RU9PD/r7+2t6LmdtvqY30QINnayhoQGXL1/G5cuXAXz2Gdje3labUXk8HnWwpPWmBGYahJqF2WYOCoXCiSsESrcMTqfTR+p1lOLmQCAAh8NR8/dsMpnUbcdEM2M4EEg9woHSrAoAHj9+fOJdYL3vZOkxc7C6uoqVlRXcv38fuVwOz58/r+vxiynLe/RowCNJEra3t/H06VO8/fbbdemKLeLASMRzLib6+QO1D2etra3o7+9Xm1Ht7e0hEokgFAohn88f2V/+PLNqZrtDbRai1xyUqvaa0tLSgp6eHvT09Bwpbp6ZmUEymTzSubkWxc1cVlQbDAcCqXU4UO6IDwwMoLe398Q/q9fAtNw51ENxaBoZGYHdbsfe3p7uNQ96vQbxeByHh4cYGhpCU1NTXY7JmQM6q3oNqi0WC7xeL7xeL27cuIF8Pq9umTo7Owu73X7mJRhm2v7TTIzQBE1L53k8pcXNSliORqNqcXNxcb8WNYxcVlQbDAcCqeVaVqWYtNJlREpQ0TMc1GtZ0cHBAUKhEPr7+9Hb26u+DkbYLaneA89sNoupqSlIkoRHjx7V9aIoYjjgnV796RnO7HY7OusC1+QAACAASURBVDo60NHRAeCzLVMjkYi6BMPhcKhh4bS7n3rP1FJ5Zps50PK6XhyWleLmnZ0dRCIRLC4uqsXNSnH/WY7LrUxrg+HggsvlchgfH4fdblfviFdC7x4DQH2WFW1sbGBhYQF3796F2+0+8jO9d0uqdzhRZpb6+voQiUTqfkEUtSBZtHM2I6MMqpubm48swdjf30ckEsHk5CQODw/VLSMDgcBrd1UZDozJbOGglrPRNptNfX8Dnxc3b25uYnp6+kzFzVxWVBsMBxeYsif9tWvX0N3dXdXf1fuuOVDbwbkkSZiamsLh4eGxW7jq/RzU80762toalpeX8eDBA9hsNmxvb9fluMX0mCnRgojnbCZGHVRbLBa4XC64XC51y1TlrmrxlqnBYBBer9ewj+OiM1s4qOcyqdOKm9va2tQlSMcVN3NZUW0wHFxAsixjeXkZ6+vrePDgARwOR9W/w8wzB6lUCqFQCJcvX8bt27ePvSDrHQ7qMVguFAqYmppCLpdTZ5YODw91edwi3oXnYI4qZbVaj2wZmc1mEY1Gsb6+jomJCUiSBK/XC7fbXZddYGpFtM/wafSuvdOansuFS4ubDw4OXituVnYBU2YfKg0H3/3ud/GTn/wEwWAQU1NTr/1clmX82Z/9GT788EO0trbiX/7lX3Dv3j3NH6MoGA4EdJ47SLlcDqOjo2hqasLIyMiZvwSMEg5yuZymv1PZu/nOnTun7sBjhHBQy+On02l8+umnuHz5MgYGBtT3nF6DdBHDAWC+wZBoRL3j3tjYeGTLVKUZZfFASemvUK9NAbRgtsJqs80cGCXsFDcjHBgYOLIT2B/90R9hcXERDx48wP7+fkX9n77zne/ggw8+wLe+9a2yP//pT3+KhYUFLCws4OOPP8Yf//Ef4+OPP9b6YQmD4UAwyqD8LFvi7e7uYnx8HNevX0dXV5cm56Enm82Gw8NDTX6XJEmYnZ1FPB7H8PBwRRdbM4eDSCSCqakpvP3222rzp+LjMhxURsRBKRlTQ0MD2tvbcenSJXWgtL29jdXVVeTzebWw0whda09iti1ZuVtRfRQXN3/44YdIJpP42c9+hr/8y7/EN77xDVitVnzpS1/Cb/3Wb5W9hn/hC1/AysrKsb//P//zP/Gtb30LFosFjx49wt7eHjY3N9UlTxcNw4FgzhIOZFnG0tISNjc38e6772pSvKP3wFjLczg8PEQoFEJ7ezsePXpU8YVLzw7NQG1qDmRZxuLiIra3tzE0NFS2iZNeuwaJGA4AzhzozSzPf/EMSPFAaXBwUN0yVZn5bGxsVAs73W63oQbjZps5EHVm6jh670JYqba2Nnz961/HX//1X+MXv/gF4vE4njx5gv/4j//An//5n8Pv9+Of//mfK66n3NjYQE9Pj/rv3d3d2NjYYDggMdjt9qoGpNlsFqOjo2htbcXw8LBmH3qjzBycd5AajUYxOTmJW7duqWsYK6X3BUHrO/jKkrPW1lYMDQ0dewE368xBNBrF8+fP4ff7EQwGNeluq/d7hD5jhtfhpEFo6Zap6XRaLWxOJBJwOp1qWNC7eNNsMweAOd5fCqMsK6qGxWKBx+PB1772NXzta18D8Nlgv5prerlri5le12oxHAimmkF5LBbDxMQE3njjDc3TrxHCwXnu3MuyjIWFBUQiETx69KgmnRtrTcvZm0QigXA4XNGSM7PNHMiyjGfPnmFzcxNvvPEGdnd38emnn+Lw8BDBYBCdnZ1nXqoh6myHmZjl+a/mDnVLSwt6e3vR29urbpm6vb2N8fFxZDIZzRtRVcNsa/TNxqjLiqpV7dLp7u5uPH/+XP339fV1td7nImI4EEwlg3Jl4Lu9vY2HDx/W5E6RUcLBWQap2WwW4XAYTqfzxDvkRqfVIH19fR2Li4u4f/8+nE5nRcfVQy0G2vl8Xu3zMTw8rO4Y09TUhM3NTWxubmJmZgaJRALNzc3q1pJOpxN2ux02mw02mw1Wq1X9/8X/pNNpZLNZYabqzcoMdwDPunyleMvUa9euHWlEtbCwoL7nA4EAvF5vzb8PzbYMx4wu4uvze7/3e/jhD3+Ib3zjG/j444/hdrsv7JIigOFAODab7cTK/Ewmg3A4DJfLpQ52anUeeoeDs5yDUpQ9ODgo/Af/vMt7JEnC9PT0ib0cjETrcJBKpfDpp5+ir68PfX196n9/+fIlIpEI7Hb7ka0lDw8Psbu7i+npaaTTaTgcDvh8Pni9XjQ0NJQNqwcHB1hfX0djY6M6XX9ckCj+56Q/I2qY1ctFnDk4SWkjqmw2i0gkgufPn2NiYgKtra3qz2uxZSpnDkgP3/zmN/HkyRNEo1F0d3fj+9//vrrb4fe+9z185StfwYcffohr166htbUVP/rRj3Q+Y30xHAjmpAGxsn7+rbfeUtee1kotthE9yzlUeue8uLeDVkXZejvPsqJ0Oo1QKITOzk7cunVLiDtFWoYDZTem0i1r9/b2sLGxAYvF8tpz0traipaWFnR1dUGSJCQSCezs7GBjYwMA4PF44PV64XK5Xhv8KK9ToVBAoVBQPzunPabjfm6z2WC322G1Ws8cNi7SAE2E9/dpanXHvbGxEV1dXejq6oIsy0gmk0f2lvd4PGpY0GLLVLMVJJN+crlcxZuz/PjHPz7x5xaLBf/wD/+gxWmZAsOBYMqFA1mWMT8/j2g0Wrf180aZOahkcJzL5TA2NobGxsZz9XYwmrOGAyVE3r59W70rLgItllEpO3dtbW29thtTMpnE8vKyOhgvHpQXD9KV/1WWaly5cgW5XA67u7t4+fIlFhcX0dLSAq/Xqy7pU2Z5igd35f69dEea44KDLMvIZDJlf3bS+6L4ZxaL5UhoKBc2JEnC7u4uYrGYsCGDMweVs1gscDgccDgcuHLlCiRJUveWX1lZgSRJ8Pv959oy1YwFyaSPVCpliht9RsRwIJjS3YoODw8RDofh9Xrrun7eCOGgkoJkpdD22rVrFW9pJopqB8vFA2MRi7DPO6DI5/NqSCxdcpfNZrG0tHTm8GG329W7q7IsY21tDf/7v/+Lzc1NOJ1O5HI5XLp0CR6PR73TVW4Qr8xYKMGgNCgUB4bi81f+20nvidKfybKszmQcF0Ty+by6l/5xg2ybzYZ4PI69vT20tbXh8uXLaGxsrGqZVK1DhhkGo3qs1bdarfD5fPD5fBgcHEQulyu7ZWowGITL5aro/Mw0c2CW4CmqSrsjU/UYDgRTPCjf3t7G9PQ0bt68iWAwqNt56OW0mYO1tTUsLy9XXGh7VnoV2FUzc6DMnjQ1NdW0FqWWzjNzkEwmEQqFXqsvAD5b6rOwsHDsMrmT7uCX+1k8HscvfvELtLW14fr161haWsLc3BxaWlqwtrYGq9UKv98Pj8dTdk13ucdZPPhXZhjKnUu556c4bJz0upc+luKZjOMev9VqxezsLH70ox9hd3cXIyMj6OzsxPvvv4+mpqYTg0rp77RYLJrUZJQ+n2YZwBmhkLehoQGdnZ3o7OwE8PmWqYuLi0e2TA0Gg8fefDDTzIHZ6ieM8B6rRjKZZDioEYYDwdhsNmQyGczMzGB3d/fYRlW1ZpQmaOUCSqFQwMTEBCRJwsjIyJm6SVdzDnrtC11pQfL+/j7C4TCuXr0q9OzJWWsOlBD9zjvvwOv1HvmZMptyXKftSpfoFFtfX1eD69jYGHp7e5HNZuH1enHt2jXk83lEo1FsbGzg4OAAra2t8Pl88Hg8aG1trfjOf+nPTlqCpPxvuT9z0mMsvglQPGhQAkcqlUIoFMLg4CD+9V//Fb//+7+Pra0trK2t4dq1a1W9ZrIsI5/Pw2q1IpvNlv0zJ51r8exKcVhQtvF0u93Hhopy/91ogyQj3nEv3TI1kUggEolgdHQU2WwWPp8PwWAQfr9f3fDATANqMz0WQLxtTLmsqHYYDgRTKBSwvLyM3t5eDA0N6XYBM8LMwXG7w4TDYfT29qKvr6/mz48yCNQjHFgsllNfgxcvXmB+fh737t2Dy+Wq05nVRrXhoJJuz6urq9jf3y97rErutpcGtOKBeENDA372s5/hD/7gD9DY2Kj+Lrvdrt59VQpAd3Z2MD8/j1wuB7fbDZ/PB7fbrb6vzlOMfdqd/5PCTz6fVz9Dpb9DkiTs7+9DkiR0dXWp27+2tLQgEong6tWrx/7e457X0ue8tA6jkhkcJWQou7rt7+8jmUwiFotV9RxYLBY0NDS8FjYqmcFQXmer1arZd5DRZ0AsFgvcbjfcbveRLVO3t7cxPz8Pq9WKQCCgPqdmYMZwIFJNHpcV1Q7DgUBevnyJhYUFeL1eDA4O6nouRggHpRcYZSD8zjvvwOPx1OUc9JxBUQZv5UiShJmZGRwcHAixTWklqhkgF9cXHFeLs7m5eeyAsfgufekxTxtQd3d3Y3JyEpIk4erVq5iamsJv//Zvo729/UhNgcLlcsHpdKK/vx+5XA7xeByxWAzPnj1DQ0MDvF4v/H4/Wltbyw6qzjP4P8vPio+nLIvK5/P40z/9U9jtdmxtbR1b6F78e8s9ryd9p5QWiBf//3LPgRIqlAF6uT9z0uOUZfnYGYzT/m7xz4oDRCW1F0qoKP2ZaEs+SrdMzWQyiEajWF1dRTweRzKZRDAYRCAQQFtbm1CPTWG2cCBad2SGg9phOBCAMtBLJBK4efPmsQOaejJCOFAo+/Wn0+m6D4T1Dgfljn14eIhQKIRAIID33ntPyItuOZUuo0omk/j0009x5coV9Pb2lv0zOzs7ePHixbHHOevSHkmS4PF48MUvfhHhcBj9/f2YmJjAF7/4RQBQPzPl1tsrF2alABT4bEC1t7eH1dVVpNNpOJ1OeL1eeL1eNDY2vvY7SgfQZx38V/qebm5uxv379/HrX/9a/W8dHR2v1XVoeUzg9aBw3HeR8nvLLakqLvYu/t/i31/uv512vqU/kyQJkiRVtH3tSc/R7Ows8vk8nE5nVWGjNHDopampCV1dXbDZbNjd3UVPT4+65C+VSsHr9aphovS9bVRmCweizRyw5qB2GA4MLpVKIRwOIxgM4tGjR9jb2zPEoNwo4UCSJHz00Ue4dOmSLvv1Gy0c7OzsYHx8XJci9VqrZOZAGWzcvXv32Nmjg4MDrKysHHuMs6zrL3Xp0iX8zu/8Dh4/fozf/d3fRTKZRFtbGxKJBJaWlpBMJtHd3Y2enh40NDQce8yWlhY0NTWho6MDsixjf39f7a0gy/KxvRVK3xvFy3JsNtuJy6VKl/EUP+Zy77kbN24gGAxib28PTU1NCAaDrw0wKp2JqPbnZ539UJTu3lT6dyut0Sj+3jkpxCpBptwyqdPOV5IkFAqFsvUx1Ty/py2HqrQY/KyUAbWyZerAwIC6Zer29jaWl5chSZLatdnn8xl2wCranfbTsOaAFAwHBra5uYnZ2Vm8/fbb8Pv9AIwzKDdCQfLLly+RTCYxPDysPj/1pufzULr0ZXl5GRsbG3j48GFd7qbUe5nDaUW3CwsLiEQiGB4ePrZZUyaTwfLy8pGlPacV7J7n3JqamnDv3j38/Oc/x1e/+lX893//N375y19icHAQGxsb2N3dxd27d8v+znIDfKW3glK0u7u7i+3tbSwuLqK5uVldglRaX1F8bscNess9juLnqXRpS/FrXzzbUXycFy9eYH19Xd03v9rtc8+z9Om45UvKz88SOI4Lj8UzDcd9Pxcvmyp37OKdoUqXnhW/BsX1GIpqvoOKG/GdJ7QptQOVzl4o/6TTaRQKhSN33Yu3TAU+210tGo1ic3MT09PTaGpqUmcVKt0ytR44c6AvLiuqHYYDA1KWyaRSKYyMjByZYi3tc6CX/8/elwe3cZ7nPwABkAQIgCB434dISqIo6hZF2rJlXZZUSxnHjmMn47aJ406TtGnGSZtOJ5lMf8mk1zSTNmnSSQ9P2nES1574iB3bUnzUsmVLvHTyvu8DF0kQAHHs7w/2Wy8+fnvgIkgHzwwHIHa/c7/dfY/nfb9kKikcx6Gnp4fPq54sxQDYHJ6DQCCA69evQ6PRoKWlZUMe7snI0iSVi7+zsxOZmZmSe30EAgH09/eL8shZgjGBGOdbmFqUZQ1OS0tDc3MzXnnlFezevZsvc+fOHTzwwAMYHBxEfX39uhecEgGV3lvB4/HA4XBgYGAAXq8XJpOJz4JEMnbF0wpPp1el0dbWhra2Nuh0Oj6V7ic+8Ymw2AmWokG3wZrXSGlI9LWMxdsghljqFUsjS8oSYZr8iZUT/k5/0uuXpk7R61hurGKpf6X6Bax593w+HzweDwBIKhM5OTnIy8vjFeHx8XF+1+b8/HwUFhYiKysraQL6VrO0y2GreUJStKLEIaUcbDK43W50dHSI0mQ2i+cgWZYbsulbTk4Ompub8c477yQ1UE8uiDLRbft8Prz33nuS/PpEIJbsOfFsc3l5Ge3t7aiurkZZWZloWZKyNJJdhWnhTGmfhHUCQH19Pf7jP/4Do6Oj0Gg02LdvH95//30+UFYoYBABLVJrrkqlgl6vh8FgQElJCUKhEBYXF2G32/m9FYiiYDQa190vSigtkfSH0CELCgp4PvnCwgJ6enqwb98+ntYUrVdA+El/Z50ntMRHG/cQb2+DkrJ0ALdSQVRsfmmFjhWHIQzeFptrui+kLqJEK6VVAR95MuTmgnjOjEYjlpeXcfv2bVy+fBl+vx/Z2dnIy8uDxWJBenq6aOYoucxSkQr6H0fPwVYaz8rKCh/wnkJ8kVIONhGmpqbQ29vLzMdOsFmUg2RgYWEBN2/eDOPTsyxiG4lkeg4cDgdmZ2fR0tICs9m8oW0rDQ6OJ2jhbHZ2Ft3d3YqyUw0PD2N5eZl5LBEZfYScdbVajVOnTqGnpwelpaUoLCzEgw8+iMXFRV6gJ/WIrWOa2kOveSLQhUIheDwecBwHi8XCz0sgEIDNZsPU1BSWl5eRmZmJnJwcWCwW2b0VornOKysrUKnWUoA+//zzaGlpQUFBAex2u+zcKfEKsDITidVLroNYvbQSQdfLynQUSayAFCKZB9Y1j0ZZkQNrniJZAyyFg8S6kP+JUC4sQ/os5ikSKjZGoxFGoxHl5eUIBoNYXFzEwsICBgYGkJaWFhaLw7p+QgjnStg3qcxR5LvdbofH48HKykrY8a0kYAuRohWlQJBSDjYBgsEgbt26BZ/Ph7vuuksy205aWppo+sqPKzhuLV/97Owsmpubw3jLZJ+BZD2Mk6EccByH7u5u2Gw2FBQUbLhiAERO64hXm0Qw7uvrg81mw5EjR0TjCwgIt5+FRKX6pIX9+++/H9/61rfw//7f/0Nvby9CoRCMRiMOHz6saO0S4UloGKAFVHLsH/7hH1BdXY3HHnsMAPiXvXBnW7K3AtkZmghTZrMZGo0mTBATU1ik5sBisUCr1cLr9WLnzp24desWDAYDysrKYlo7ibheUooDIJ8NiSW0s84TtifnOZHqp9x44uWpEKs7UoWEnE+UtEAgwD+3hWXF5pjlMaHn22q18vTS1dVV2O12zMzMoL+/H3q9nt87hI55YSlgwver3DwvLCxgcXFxnUCtUrH3yGB5L6RiNjba6JWiFaVAkFIOkgyyaVdpaSl2794t+zDYLIFYG4XV1VV0dnbCYDCgpaVl3UuCvFQSuQuyFDZaOfD5fDytqrGxEcPDwxvWthDJ8hyEQiFcu3YNer0ezc3NsoK1zWbD7Oys5Hn0WJQIi1LXnGXVbmhoQCAQgEajwblz5+D3+6HX6yUzDJGd0MfGxmCxWLBr1y6mR5Eud+LECfz4xz/GY489FibYCvul1+uh1+tRWlqKYDAYtreCRqPhg0NZipdQYaCtv8LfT5w4gTfeeAN5eXm4dOkSHn74YWzbti0hmYmSoXAQiHkxpMaixItBC8Uk+Jem+kRyHyZKqYi0LC3cS5WlFQlAmh6l0WiQn5+P/Px8qFQqLC8v87E4Pp8vLBYnPT09qsxSBEJPB41o98gQjotWLpRmlaKPK5UbtiKtKKUcJAYp5SCJmJiYwMDAwIZu2rWV4HA4cP36ddTX16OoqIh5DuvFsZHYSOXA4XCgq6sLO3fuREFBAb87bTKQjJgDt9sNl8uFPXv2oLS0VPb8xcVFjI6OinKrI8nYQ//OeoEKs82Q8+x2Ozo7OzE8PIympia8/PLL+NrXvrZO6KbXEcdxePvttzE9PQ2z2Yzx8XGMjo7iwoULMBqNYX2j18CBAwcwMTGBt956CzU1NSguLmYqz0K6hzBTjNfrhcvlwujoKNxuN/x+P2ZnZ/m9FZQqR6WlpXjsscdgs9lw8+ZNZGRk8F4JlqVdjONO6lN6vVjHxZAsC7xYf2mPAisjkRynn/VJ/xapYhFP6pSUQJ2Idg0GAwwGA0pLS/lYHBLczHFr6YBzcnL4/SMA+WxXQtogoR6xQM+zEo8Rff2Fu33LrXWxuoU0KTGFIy0tDXNzc9DpdHC5XMy4jM2GVCrTxGHzXe3fAXAch+vXryMQCGzp3WvJAzTelgaO4zAyMoLx8XEcPHhQ8uZPZkAwaT/RAjrHcRgdHcXY2BgOHTrEz0cyqD0EG932zMwMuru7eWu3HDweD4aGhkSDd6PhULOEfyHotbC4uIjXX38dDocDeXl5KCkpgdlsFqXqCIOSSXxAYWEhbt++jfr6ejgcDgwPD4dlPWL1o6urCxUVFXjxxRdx4MABFBQU4NixY2Evd6l1q9frkZGRgYKCAn6naa/Xizt37oDjOJ6iQe+tIJwrgoyMDJSUlODs2bO4ePEijh8/vu48ViCrGN9cCKlYAbqs0OIuFZ+gFLEoFdF6R+Riq+QCkGnlU0m7Yl4isb4pqVf4zojGuyLXZ6myarWaVwZCobVMb2R/hYGBAeh0urBYHLH7lNRN3j1iGaRYRgkpD4rwu1j8C6teqTEL+yeXYWpychI6nW4ddVl4H7E8FHKxGfTv8WJApDwHiUNKOUgCVCoVKioqkJ2dvaVpQiQ4Op7Kgd/vx/Xr16HVatHa2irLf0xmQPBGtB8MBnH9+nWoVKp185HMsW8UrainpwevvPIK3G43HnroIczNzcmW8fv9GBgYWKc0rq6uYmpqCj6fD/n5+UyKTrSCG+vY6Ogozz3u6+vDrl27MDMzA5vNxlvpxeoMBAL8S/SDDz6ASqVCYWEhVldXJYVip9OJ3t5eNDc348UXX8QDDzyA6elpTE1N8dmspIQIVn80Gg0qKipQWVkJv98fJkylp6fDYrEgJydH8iV9/Phx/OAHP2C+zOWEPKVWdtZYSApQWqFjxYUoiRWgy0bSX9KnjaZGxVo2WkWHjscQfgqDduNNj4qkrEajQW5uLnJzcwGsGRVcLhdGRkbg8XhgMBj4HcnT09OZSpYUNVAOYmuSPiZXtxJFmdTBCqwndcu9z0Oh8N2+SZuRrnmh4kArFqWlpYrjHlIxB4lDSjlIEsSyESmFnBVpIxBv4XRxcREdHR2oqamRTEspxMeZVuR2u9He3o7y8nJUVFSsu97J4P0TbITn4Nq1a/jpT3+K3NxcFBQU4LnnnkNZWRnuvfde0TKhUAiDg4Pr+L4ejwdvvPEGFhcX+ZdZc3Mzamtr+XPiHey6urrKH3v++edRV1cXFgMgNYdkI7PFxUU0NTWhq6sLx44dQ3l5uWRMxPLyMtLS0lBdXQ0AWFpagk6nw+LiIt9XUl7s+SH0YNAvfpYwZbfbMTw8DI/HA6PRyFteiadCrVbDbDbj6aeflg0IjQTxErRpK2809SoRzoTKBes3JQKWmAKTCE+FHCKNxyDfCY9fSZ9Za5X8L0XlIXMlZ7mnYTAYkJmZicLCQnAch+XlZdjtdnR3dyMYDCI7OxvZ2dl84H4oFApb54mK2VCynqW8FUqFdxKQzFrHLE+GXP1i/SZKBr3jd3FxcUQB0SlaUeKQUg62IIjFPtkcwHimVR0bG8PQ0BD27dsHk8mkuNxmoBUlon2SprOpqUlUkUym5yBSak6kWFpaws9+9jPU1tYiFArB5/OhoKAAt27dkiw3PDwMt9u97veBgQEsLy+jsLAQXq8XGo2G3x+BZBURCl/CsUWrNFRWVuLGjRtIS0tDRUUF2trasHv37nU7CbOg1Wpx8uRJvPvuu8jLy8Orr76Kr33ta8jPz5ds02Kx8C/dr371qwDWKFlWq1XWMskCSwAQCgmEz11WVoZQKISlpSXYbDZMTk6C4zheUTAajaiqqpJtT4ho5z0W630ivRhidDSp+AC6DqHiRj4T5alIVFk5CMvS92M8hGgxBU5InSFKCdlXoaKiAqFQCE6nE3a7HSMjI7wQTbLFJWo+YlnPSuqm40GEazVahUdMWWYZNcn/JpNJNLZQDClaUeKQUg62ID5OykEwGMTNmzcRDAZx1113RTymzeA5kOJxRgqO49Db2wuHwyGbpjPRAroUEqmYTE9Po6enB7m5ucjPz8cbb7yBsbEx/OEf/mGYlYnG+Pg4nE4n89j8/Dz0ej0GBwfx+uuv44tf/CICgQCWl5dhsVhE17FQUADEhTYCodBmtVpx991348UXX0RlZSV6e3vxZ3/2Z7xQIWfNzcnJwfnz5+H1etHd3Y3JyUns3btXUgDNzMzEwYMHce3aNf7FX1dXx1tCCV5++WXcfffdfCIEuf6wLMCknLA/JP88sEaNstvtYXsrEApSZmZmmDAmBlbbsVA3kkHriUagZXkxiLWVLsuyFJOyYvNLK3qRUFjkoISmJHbNE9kuHegrhBJlBwBycnLCUqb29/fD5XKhvb09bO8Q4iETs+ZH0u9YykY6n0IDSSwKoNR9yjI46HQ6VFZWKu4ngd/v37Ixm5sdKeVgC2KzbIQWaz8IbaasrAyVlZVR0aSS7TmIp3KyurqKjo4OmM1mNDc3y87Hx81zIFSMWltb4fV60dXVhebmZvzqV7/Cfffdh5qaGmbZubk50XgEtVqNgoICTE5OorKykhdYMzMzYTQaIxLqlATKOZxbKAAAIABJREFUCo/V1NTg6NGjqK2txfnz58PoEFL0E+GxzMxMnDlzBq+++irOnj0r29fa2loUFRXB5XLBYDDwsU3Cvl65cgU+nw8PPfSQIou3XJssaLVa5Ofn8zuYut1uOJ1O9PX1IRAIwGQyhe2tIGxTyTVhWdppnjv5jVjd5a6XGKL1NsghEdZ5Mn6p56KSay6lEAt/FwrAclRH1vURHtvsngzgo/FqtVqegmSxWMLWN0mZSuIVxLKFCRU5sbaDwSCT4hfrmFnHCa1IDvFsW6VSobq6OunGzhTCkboaWxAajWZTKAexPHCnpqbQ19cXcxrXj0tAstPpRFdXF7Zv385vVLVRbUeDeMc7+P1+dHR0wGg08orRvffeC4/Hg97eXpSUlGBlZQV33XXXurIulwvj4+PMeslLrLa2FuPj45ifn8e2bdvQ1taGb3zjG5JWaylEwuNWq9cypLS2tuLSpUv45Cc/qaicEPfccw+++93vwul0wmKxMF31wt+IBV8si8ypU6fwzDPP4FOf+pSkkBgIBESpMHJC4NLSEt59910MDg7CaDSitbUV27ZtQ3l5Ofx+P1wuFxwOB0/RIFZZsSwxNFgeBdZzUWh5Z/WTfEYbKxCtkJRIpSKeVKNoPS9SNCnWDsliXgy5duWQyFgA4XlZWVnIysriU6a6XC64XC5MTEwAQNiuzWTscv0SZg2SoqSR78JnAe01UqJYEK9OLN6MSO+J0tLSVNzAJkRKOdiC2Mqeg1AohDt37sDtdqOlpQU6nW7D+xBPxENAHx0dxcjICA4cOICsrCzF5ZJJK4qFgkGDBKLX1dWhuLiY/z0zMxMPPvgg3G438vLy8OKLL+LcuXNhZT0eD0ZHR5n0E9ptferUKczPz6OoqAg/+tGPUFJSIjm+aII4WcdIPWfOnMHPfvYzpnIgNZ8qlQqZmZl46qmnsLq6uo5nLlWW7g8RJlpbW/Htb38bs7OzKCgoYJYVCmwk8Jh4IqRAhPRf//rXsNvtyM/Ph9frxSuvvIJHHnkEhYWF6/ZW8Pl8cDgcGBsbg9vtXpclhjUWqXEqRSyxAqQ8IJ3xSIx2ttmUCmH/4tGu2BoVS/8pdw0iUeTjobzJgaxzVr/UajWsVissFgsqJbJ8ZWdnw2AwrFs30Sg0wrUVaZCwUDEj72QxOhqpW+6eUNK2xWJBfn6+6PkpJA8p5WALItkCcbT98Hg8aG9vR0FBARoaGqKiEdHYyp4DYbxFa2vrlnKrxksxIR4kqUB0g8GARx55BE899RSeeOIJ/nfC+VUS86FSrW38U1RUhMLCQvzgBz9AT08Pdu7cCSD8pRetYMY6JhQajxw5wnzhKp3LT3ziEzH3R6gsHTt2DG+88QY+85nPiPaJ4zhMTk6ivb0dPp8PWq0W27dvx913382kR5FyDoeDV8SuXr2KnTt3Ij09HXfu3GF6xtLT0/lrw8oSQxQFk8m0jvaQzFgBmlPOihWQKyv8jZRlCcNCalQ0sQLJou3QZaPtczQeBTGaGV2HEEoUC3JMLH6C7pdWq0VeXh5PsfN6vbDb7RgdHYXH40FWVhbvWcjIyIg7XYg1PtZvZEzRKqZyVDRyjOM4pKeno6KiQvQ8OSTLMPa7gq0jjaTAYysqB3Nzc7h9+zZ2797NB3TFqw/JVg6iuRYrKytob29HSUkJqqqq4qIobSRipRVxHIeenh64XC5FHiSj0Yhz587hrbfewoULFxAMBjEwMCCqGNDCF82LPnv2LF555RVs37497Byx62m329He3o75+XkUFhbiwIED6yzofX19yMvL43+nA++0Wi2TFiWFeCoqBKQ/p0+fxo9+9CM88MADMBgMYbvDkr6TuI+srCy8+eabeOKJJ3Dnzh1UVFTwL3ahQEzmTjj3s7OzUKvVYXFFtLBGC3FmsxlmsxlVVVUIBAJwOBxYWFjA4OAgb3W1WCwwGAyy1m4xjnuyYgXElEGp9UeOS1lsybNQiiLFUio4jpN9lsfToyAUqJMRgCxnWZeqWzi3pA7WDslyClxGRgaKi4tRXFwMjuOwtLQEh8OBnp4eBAKBsI0GhUajWD0hch4Fsr9KNHWLzTerbbVajerq6ojSltLw+/0xMw9SEEdKOdiCSEtLW7eDYbL6IScYkyBTu92OlpYWyew70UCtjm+2oGjaj1RIJopSU1OTorSWmxGxWGv9fj/a29thNptx+PBhxYrRZz/7Wfz5n/85OI7D0NAQPB4P8zwlQvOZM2fwR3/0R3z2IKlyHo8HFy9ehFqtRk5ODubn5/HGG2/g/Pnz0Ol0/Evvv/7rv7B9+3Y8+uijYeVZnHWav86inkRCFxJC6bUxGo0YGRnB008/jYKCAtxzzz0oLi4OK+twOBAKhVBZWQmn0wmHw4GMjAxMTU2FWf3oNnNyclBUVISZmRnU1dXhypUrKC4uxo4dO8LGSMqKPUdIMLHVauWNCsTqSjaqIoGfOTk5YZlLWJZ5pXSTaGllrHaVllVy3aT6JJxDqbHLlaUVODllRkkAMqtcsjwZcpAqS4R+IUVKjiJG182KESL7JwBrWb5cLldYylSiDJNMYJH2W8lxQDwgOZ4ByABQXl6+bs+TSJFKY5pYxG9r2xQ2DJvFcyD3QPD5fLhy5Qo4jpNNyxkttpLngOM49PX1YWBgAC0tLVtWMQCi9xwsLi7ivffeQ3l5OXbs2BGRx+TkyZOYmprCu+++y2/qRUOpQF1ZWYm8vDxcu3Zt3TEa09PT8Pl8yMzMxHvvvQeLxYKVlZV12ZHOnDmD1157bV1/CISWX2GQLPmf/NECCF2f0Ooq/CPHiODBsiCT67awsICrV6+ioaEBU1NT0Ol0ePPNN9cpXHq9nhfmnnjiCVgsFqyursrGHahUKpw5cwY7duyAxWLhM1DRlCI5AXBychJf+cpXwn4nVtfGxkbs27cPBQUFcLvduHHjBtrb2zE0NASXyxW2OzItpAoFXzJv5I+kmqXnlvwpoVWwEKvAGgmHPJay9Bol80j/CY+x6pVap0KFXGydJtKjEMtcCo/TtCI5Og1Zj/Q9L3weqNVqWCwW1NTUYN++fdi+fTt0Oh0mJydx7do13Llzh38mkXlOS0vj71PWfCtVhsW8bFKIdM5yc3Pjwh5I7Y6cWKQ8B1sQm0U5SEtLE7Xa22w23LhxAw0NDQkNOIqW1hPP9pW8xEg2nqysLDQ3N0cUXLcZEY3nQEl8gRS0Wi2am5vx85//HE8++eS647SFXigAsK7T/fffj9deew1HjhxRNBaNRoPLly+jrq4OwEc5wUk7Bw4cwPT0NAYGBlBZWQmdThd3ShBpVwpSFmLy8p+enoZGo8HevXvx4osv4r777sPS0hLsdjsfqM1xHLKzs1FRUYGpqSlkZGRgZmYGOTk5YRuaiVmWDQYDTp48iePHj2N+fh49PT3Yv39/WDm5sRQWFqK3txcjIyOoFORBJ3OkVqt5ClLl/wV+ulwuTE1NYWlpCRkZGdBoNGGGCRaPnUWNoiE2TjpWQEy4kqKaxOKpkEKyykrFCgipZ2JxBHJxAvRvNGdeSb8ihZgiJbz+8aybID09HcXFxXw8DkmZ2tvbi9XVVZhMJuTk5CA7O1s0ZaoUzUcYO0QUChpSazeScen1epSVlSkuL4XU7siJRUo52IKQEso3uh/0plQcx2FgYACzs7Nobm6O2XUoh1geyBvVvsvlQmdn57psPFsZkXgOOI5Dd3c3lpaW0NraGvWmNQ6HA7t378YzzzyDz3/+8+uEByVCMTkXWLP0P/jgg/irv/orXnhkcZMLCwuh1WqxvLyMpqYmfPjhhzh69CiKiorCzvd6vdi+fTt+8IMf4OjRo9ixYwcaGhqY/YmVEiQ2TqX1pqenIxgMory8HGfPnuUtwFqtdl0djY2NyMvLw9TUFMxmM2pqavj5oqkntBBHfjt16hR+/OMf88HPSjnfarUaJ06cwMWLF/GFL3xBdpxarRa5ubnIzc0Fx3FYWVnB6OgoFhYWYLPZePoGS5CK9llCxhipUiFsl0U1EdYvtALTvyeCepPIslIQKytU3iLxCojFtogh0mNkjcZK6VFKRVOpwlOmBoNBLC8vw2azYWxsDCqVis+CJEyZKtYmPd+0cqV0vllrl9Qt9CBVV1fHzTCWohUlFlvbfPk7is2yzwHtwfD7/bh69Sp8Ph9aWloSrhiQPmxm5WB8fBxdXV3Yv3//x0YxAJQLAKurq/jggw+gVqtx6NChqBUDt9uNkZERVFVVgeM43LlzJ6wvci91mtITCoVgtVrxzW9+E36/P4zSQ/7Ii0+v1+PUqVPIyspCRUUFenp6cPr0aaSnp4cJbe+//z5qamrQ398Pk8mEzs7OdfsvxCr8R2NdZpUrLy+HwWDA/Pw8iouLMTs7i6KionXufjK+8vJyNDc3Y8eOHdDpdGGChXDu6O9kLg8ePIipqSlMTk7y88Ci7ggtl+S3U6dO4eLFi4rmjxYGSUrUoqIi7N+/H1arFS6XCzdu3EBXVxdGR0extLQEQD7nvJzyGQ3kqCb07/T6FAqN9JzS80vTeqSoNdHGTciBlI2UuqKkXdZ1EHonQqGQKEVKuF5psOZWuE5jpUgpoSKJQavVwmw2o7q6Gvv27cOuXbtgMBgwOzuLjo4O3L59G+Pj43C73RGvUaUKotK1W1FREVdqcUo5SCxSnoMtiM1CKxI+9MgmXhttHd+stKJQKIRbt25hdXV1y6UpVQI5AQL4aP+C+vp6FBUVRd2Wz+fDwMAAP89nz57Fb37zG6ZVPpJ+Equ02DHhdbVarbj//vtx+vRptLS0rNtZeXl5GQsLC9i1axdefvllzM7OwmQyYWhoiN+7gua5K+mrEotpNFbcjIwMnDlzBn19fVhYWEBdXR3q6urC+qVWiwf7R2oJ1Wg0+O53v4usrKywsix6DV3vrl27sLy8jMHBQX6HbJZFmNTHmlsiuJHATuCjvRUmJiZE91aQG2usFvZIg3nF6mV5vKTKsp6ZcuuTdS7wEb1Ors9CZVLsGiVinuWg5DpIUaSUKObRUKTknq+sORGmTFWr1XC73bDb7RgeHobX60VWVha/xuVSpkbathD0nBQUFMS02SkLqZiDxOLjJbH8jmAzZSsKBAIYHh7G+Ph4xJt4xasPm81zQPZzKCoqQmNjY1RWMqUQo3MkGnIv48nJSfT392P//v2SGTbkEAgEMDAwELbe77//fnz+85/HV77yFd6KHWkfYzl2+PDhdb9rNBr+WnzqU5+CyWRCIBBARkZG2HliL34pJZfuDy28EYsm3YYcTCYT9u3bp6hNIZQGN9I4fPhwVPWq1WqcPHkSly5d4pUDWhiOhraRkZGBoqIilJSUIBQK8YJUb28vgsEgsrOz+XSSZH4jsb7Gohgkg/KjhKYkFXMhfBZLKcAAwowlSq6fFDaK0hNp2XhQpOj7nq5f7LlPrPZ6vR6ZmZn8GicpU2dmZhAIBPi9Fcxmc9gzJJ7xE1lZWZIbTkaLVMxBYpFSDrYgNovnAFhLy8lxHFpbW2PKWRwtNpvnYH5+Hrdu3Yr7fg5y7W/03Eu9+O7cuYPl5eWY4gtIXSRlqZBqUlFRgZKSEly9ehV33XWXqGAcT0s7OSYmDGRkZGDbtm3o7e1FcXExVldX4ff7UVtbi+Hh4bgqKuTFH43lmY67kOK5x5v6EYuwfPr0aXzzm9/Ek08+GTFtQ2wsRCglzw+9Xg+9Xo/S0lIEAgEsLi5ifn4e/f390Ol0fNAn2dGWxbem24qXUqG0fCKFbLmydCpVmvsvpPfQx8SEYDmLO90Oq1/RKLKsfrHqjvY+iUbBE/YzmmulVqt5ZYDjOASDQT498cjICE9XdrvdyMrKYnozIm1bq9Wiuro6IcarFK0osUgpB1sQm0E5WFxcxPXr16HT6bBnz56k9WMzeA7IC2pgYABzc3M4cuTIOotxIttPlnJAv1RXV1fR3t6OnJwcHDp0KOYXwsjICJaWlta1FQgEeGpRa2sr0wpPrwmlQjGgbJMkGmq1Gnv37oXJZMLIyAjMZjN27NgBq9WK0dHRuCsqSvojprxJUVKUWLSlgmfJOcJ6WYGPkY5lx44d/I7YJFsU6a8S4U/YV6fTiWvXrmFqagqVlZU4cODAOgukRqOB1Wrl0w17vV44HA5+R1uj0cjTM7RarSgdTGw8Qgu7sK/Cc+j6iEISzVoSzoXYsUR4I5SUlZq7aL1UZH2S9S7Vb6FipxSxeiukECuFSuo6C5UptXpt3xayxpeXl9Hd3Y2xsTGesiOkIAEfyR5ic0s/G6qqqmIyEEkhRStKLFLKwRZEsgOSx8fHMTg4iIaGBoyMjCStH0DyPQfA2gPx2rVr0Ov1OHLkiOjLKBGIVIiNF+jgP5KRafv27ety2UeDqakp2O12ZrsqlQonT57Ev/zLv6yzHkkJxeSlS/YoUKvVKCgoCMu8I0X7EROKSTmtVosdO3bwuy5zHCepvCZC+Jc7Fs82lVoT6TVKK2r07wSh0EeZTsg1v3jxYphyoLS/pG6Px4NnnnmGVzrn5uYwPDyMz372s+t2ohX2mVCQioqKoFKpeIvr1NQUQqEQL0SZTCZJRV1qDln/E0hx22lBWMpTwhKEI+HcR4pkCclCIZg1Nrn3hpLdplkByOSel6o7kTSnWBQHrVaLjIwM7NixAxy3ljLV4XCgr6+P39uEzvQlbEtoKAOAkpKSmCilclhZWUlo/b/rSCkHWxDJ8hwEg0HcunULfr8fra2tohvgbCRiefnEA4uLi3C73airq0sIr1IOyRq/8MU9MTGBwcHBuMWc2Gw2TE9PS7ZrsViwZ88evP322zh79uy6Polhbm4OFy9ehN/vh0q1ls3m1KlTMJvNUQV/sugUYsdYQrFUzIiQPiTVH6XHoqEhKa03kjUoFNoiqXf79u34m7/5G6Snp2PHjh04dOjQupSqdBu0MDw4OIilpSV4vV50dnbioYcewtTUFCYmJlD5f/soKJlDsrcCsObJcjgcmJubw+DgINLT0/kdm4UZ22IVlMUgnE+WQKykXTn6DkupkPOwxdujoLSsXHkl/VK62zSLPqVkt2mWxV2ub7F6FJQoJUJlnKRMLSsrQzAYxOLiIhwOB8bGxsIoSkajcZ0RxGw2x8VIJIWVlRUUFBQktI3fZaSUgy2IZCgHbrcb7e3tKC0tRVVVFf+wS7bVPpm0IhJ0SwK+koFkKQek3Vu3bmFlZQUtLS1xcR8vLy9jfHxclC8vfBmfOXMGL7/8Mq8cSIG8WK9cuYLMzEzMzc2hrKwMq6uruHnzJlpbWyXHGekx1oucptnQgharXqFQRiyVUlQJYRm6XinEIvxHK8RFsnbHx8fR09MDlUqFlZUVdHV1YXl5GadPn17XB3qdCOfL6/VCpVKhoqIC/f39/LXw+/3rAjLpesX47RqNBnl5eSgoKEAwGITH44Hdbsfg4CC8Xi9MJhOsVivMZjPGxsZw7do1cByHAwcOYNu2bbJzQdNfIpnHWLjtkQjoYl4gVp/Vavl9AaQQq5AshXjTheg1GI1HgXgnhOuapQyLeYaUjisQCIg+VzQaTVimr9XVVTidTszMzKC/vx8ZGRl8AL/ZbA7bJDFRSMUcJBYp5WALYqOzFU1PT6O3txdNTU38w4H0I9nKQSwu72gRCoVw+/ZteDwetLa24r333tvQ9oVIxviBNWvpxMQEKioq0NDQEJeAM6/Xi4GBAcnNpNLS0nju9b333ovvfe97sNvtyM3NXXe+kAYUCoUQCATgdDpRWFiInp4euN1u7NmzR9RLsdHxAFLHhOMgY4sEQpoEqY8WMlgCcbScb6mxRFPvjRs3YDQa0dDQgL6+Ptx7770YGBjAXXfdFRYvIMVBB8AbNgKBAO6//3643W6kpaXx6ZeV9om2tJNjaWlpvMW1vLwcoVAILpcLdrsd77zzDt544w2YzWakp6fjxo0bePjhh7F//35Z5SuaOSZlxRBPIZrVjhTvXWyNk08xBVjMIyTWL1YbifB0yB2PlSJFeySkvBmstqXihIRlyfNV2AarbzqdDvn5+cjPz4dKpeIpSENDQ8jPz0cwGER+fj5yc3PjureBEKmYg8QipRxsQcRDEFOCUCjEZ55paWmBTqcLO07zzpOBjZoLAq/Xi/b2duTn52PXrl0b3j6NZHgOnE4nuru7YTabFfO/5UBSlkopBmSchM6Wnp6Oe+65B6+//joeffRRZjlirVOpVNBqtcjOzsbKygouXLgAjUaDhYUFVFRUrBOMlbxsxRCtwBxPYZqul55XJTQGYd30d6FATHsqaEWGhUiFVlJvY2Mj71li1cNxHMbHxzE5OYns7Gw+9Smp12q14ty5c7h06RKcTif0ej0++clPIisrKyLhjW5Xqmx2djbMZjNefPFFVFZWwuv1wuPxgOM4/PKXv0RhYSGsVivS09OZFnhSNx1PEIsgnCxBV44eJSwrpuRJ3ZfCPoiB5bWTe45LeQJJe8nyhChpWyz+Qtg28RywxiVGOyNzRxTiI0eOwGq1wul0Yn5+HsPDwwiF1jaczM/PR05OTtySZ6RSmSYWKeUgBSZIrv78/HwcPnw46ULwZoDNZsONGzewa9cu5OXlJbs7ADZeQRsfH8fQ0BC2b98Ol8sVlzpDoRAGBgbg8/mYx2n6gnC8Dz74IPr7+0XLEaGYlDly5AguXryIpaUlcBwHg8GAxsbGsJcr62XNEoqFoF36rHM2kydCSZti4yTHpLyGcvWynie0x0JYV0NDA15++WXk5eVh9+7dmJ2dRUVFRViMi1qtxqVLl3DlyhXeU1JcXIyjR49Cq9Xyfdq5cyfq6up44UJOWIkXN97lciE7OxsTExOYn59Ha2srpqam4Pf70d3djUAgALPZzFMztFotP8c0fUfsk+6XmCCcLFoO6QML8egXOU6fp0SRYlG3xIRi4KMg8UTO50YoDgQsJYClqAk9CkKvVk5ODv9eJFmQ6uvr4ff7+Tiy27dv816HvLw8mEymqGWLFK0osUgpBymsw9zcHG7fvo3GxkYmXeN3DRy3lm9/enoazc3NYUGGwnOSoUBtlOeAUKm8Xi9aW1vhcrngcDjiUvfIyAjcbjfzGBnfysoK7ty5g7a2NiwuLmLPnj3IyspCU1MTmpqaRMvRyM/Px4MPPojZ2VmoVCoUFhYqcnsrEYqlXuS0BU7OvU+3GW9PhBykLLjxoLKwzhE7plKpUFVVhePHj+Pq1atwOp2or69Ha2trmDXdbrfjww8/RFFREQKBALRaLaampjA4OLhujWg0GphMJtnxxFNQbmxsREdHB8rLy3Ht2jXU1tZiz549KC8vR3l5Ob+3gt1ux8jICNLS0pCTkwOLxcJvsieEmCdDjtsuBC0Mkj4nI2A2WQHIUnQ9qaBrohyIUXyEsRViFCk55VIK8VYcQiHlKbHptjMyMlBRUcE8V6vVorCwkA9Q9ng8mJubQ39/P5aWlmAymfhdnVnvVjGkaEWJRUo5SIEHx3Ho7e2F3W7f0Fz9mxmBQABdXV3Q6XRoaWlhPuRpd/9GIpaXi1L4fD60tbUhLy+Pp1LFq92JiQm4XC5Jvrvf78dvfvMbLC0twe/34/bt25iZmcH58+fD0k/S5cSg1+tR+X+ZaVhlE0kJYrn3lVCChOuOpvMIjwnr3wyxAvGqV61Wo6GhATt37gzjoxPBKxQKwW638wLus88+i/vvvx9arRY2m40ZKyD8X0x4i1ZgZY3n1KlTcDgcGB4ehtFoBMdxOHfuHH9co9EgJycHVqsVHMfxeyuMjY1heXkZoVAIs7OzsFqtzHUv1q5Un+nxScWyscZLKxcsqplYW3Q9ifQoRNOuXN1SQj/5jHQ+hcdIHVKKBatdILo5E44nkjlVq9WoqamRpHIJkZmZiYqKClRUVIDjOCwuLmJubg6dnZ1YXV2F1WpFXl4erFarZJKLFK0osUgpB1sY8RRIfT4fOjo6kJ2djSNHjqRoRACWlpbQ0dGB6upqlJWViZ7HEuA2Con2HDidTnR2dmLnzp1haeOU0JkCgQCGhoYwNzeHoqIiVFVVhc3R/Pw8ZmdnmWWF45qenobL5UJeXh4GBwexf/9+2O12zM7OMq/LZosHkIKSeqOhhtBlxIRisftcbJ6iFaTiZYGnKUnCeSBezkAggOrqavT29qKqqgqFhYXMGIVordFEARET3Gh6BqkjKysLn/vc5+BwOPD8889jYmJiXZ52YZvCvRVWVlbQ19cHn8+HW7duIRQK8dlhTCYTT2/ZqABkemz0ehRTflnUFaGlnQVynKVYxxo7Eet8RfueVPLMkIq9iLRvrH7SBhlybSKd04qKiqgNiSqVik8LXFtbi2AwCJvNhvn5efT19UGtVvNehezs7LA1kqIVJRYp5WCLgnBq4xHcQ7j0tACoFMmymieyD1NTU+jr68PevXv5fOZiSEZQ8Ea0PTY2huHhYRw6dGidhUbu5RYMBvGLX/wC3d3d0Gq18Pv92LdvHx588EGoVCosLi5ifHycP394eBgdHR3weDyor69HU1MTHwC/urrKX9+33noLFRUVUKlU8Hq9TEummEAnJRCTMoFAICxjBxCbgJEoZSTSNoU8YSF1R6kHg2UVZt1zQqVRCRVFrt1IqCgmkwnHjx/HpUuXkJ2djd7eXpw+fZpJd4jFGi1FLZOrm+y8fOHCBTzyyCMIBoPrrKMsRYbjOOh0ujAKktPpxNzcHAYGBpCens5TkDIzM5nXJVG0nEiuEUsJkBKC5WhMwjUo9vynhWAldD0lYyaJDsSOJ4pCFc1xJfd5MBiERqMJK0sr48I2gDWFnOywHA+kpaXxWZCANaPl/Pw8RkdHcf36dfzrv/4rdu7cifPnz0dEK3rttdfwla98BcFgEE888QS+8Y1vhB1/+umn8fWvf51PSf7lL38ZTzzxRNzGtRWRUg62KEga0ViUA47jMDg4iOnpaRw+fDgqLZw8iOKvncvrAAAgAElEQVSVgSAaxLMPoVAI3d3dWF5eRmtrq6Lc/clUDmKxWoshFFrbv2B1dRWtra1MCoOc52B4eBjd3d2oqqriH+IdHR04fPgwrFYrhoaG+PITExN44403kJOTg6ysLD6H/bFjxwAABQUFUKvV8Pv9qK2tRVdXFw4cOLBOkY3Wuk/GsrCwgKGhIahUKmRmZjKFLZYFnhZ+aEE80v4kyhMRi8Aixssmwp7S/rIs/7SSIbQuRyrQHjx4EDU1NZifn4fBYEBJSQnGxsYkKRg0YqU/KVEq8vPzUVlZiQ8++IDfY0MJzYTUo9VqkZeXxwtRKysrPGWJ7K1gsViQnZ0dFowdaZ+B+MYC0MJ8rJZ7VoyOkrK0N0rYXyXUqFAoJPrOSaYiFsvxUCi07lkvfJ7R/TYYDCgtLRVtKx5IT09HaWkpSktLwXFrmw++9NJL+NM//VMMDw/jj//4j3Hy5EkcP34cVquVWUcwGMSXvvQlXLx4EaWlpTh48CDOnz+PnTt3hp33yCOP4Ic//GFCx7OVkFIOtijIXgd0elGl8Pv96OzsRGZmJh/YF20/YlVSYkW8vCg+nw/t7e2wWq04dOiQYk/Ex8lzIEzV2tjYKEk7kWrXZrMhLS0NHo8Hf/mXf4m//du/hVqtxvT0NDo6OjA+Po7s7GxUVVXhzp07MBqNWFlZwdzcHLZv347BwUE++NtoNOK+++7De++9h4KCAnz44Yf4+te/vi5TTbRW+GAwiPHxcTgcDjQ1NUGr1fLCVl9fH/x+fxiFg6wzqcBPMSoM+c7iKyuJ4UgU9SlRsQJSypNcWalATykBzmq1SloznU4nrl69irm5OdTV1WHPnj38czQR1BsxnDhxApcuXeKfv1JlhQoTSzkTUpBCoZDobraEgiTsM8uaTwuEkVr1Sd0sCzZrHErKKj0eab+iVXbp9SdHNxPWLacYsZBoxYGcowQajQbV1dUbyhhQqVTYt28f9u3bh29/+9vYt28f/uAP/gAXL17EP//zP8Pv9+PYsWM4efIkjh49yis6V69exbZt21BdXQ0A+PSnP40XX3xxnXKQQjhSysEWRSwbkDmdTnR1daG2tjbmnX03w0ZoREiLZYdeu92O69evo6GhgbfGRdJ+MpWDSF8yYnA4HOjq6lI0B3LtFhYWIhgMIj09HfX19bh27RpKS0tx6dIlTExMQK/Xw+fzobe3FxqNBhzHIRgM4je/+Q2/d4JwTquqqlBSUoLt27ejp6cHi4uLYX2J1kIfDAb5PjQ2NvIvR4PBgKysLJSWliIQCMDlcsFms2FwcBDp6emwWq28V4E1N7TwIZwrORoFSygWfkoFz250rMBGxiAI25LKGCVGqVKpVFhaWsK//du/wev1IjMzEwMDAxgcHMRjjz22bp7pemIZD6tfx48fx7//+7/LPj+lFCFWu0QZIPs8eL1eOJ1OTE9P8zu6k1STUpm65O4rcg4NFtVHaHGXi4+IVQiWQqx1C/vNijOT2wFZat2StsmzVczDJkYJjFVxCAQCimlSlZWVURsm4wWVSoXW1la0trbi29/+NlwuF95++2288MILaGlp4ZWDycnJsNi00tJSfPjhh+vqe/755/G///u/qKurw/e//33JOMPfBaSUgy2KaIRyjuMwOjqK0dFRHDhwIMzyupH9iDdieVlwHIeRkRFMTEzETK1KBuLVNlkXrPgCFuQsX+Xl5Thy5Ag++OADbNu2DW+//Ta+/vWvo7e3F0VFRVhYWEB+fj5mZ2dRXV2NyclJfjfNGzdu4PDhw3w/iGdIq9XCaDTiscceg8fjYVpACZRYAL1eL+7cuYPCwkIUFRWFHROWJTxx4rb2+XxYWFjA4OAgvF7vutz08bY8y41FKT2DpvQIBRDW/CXL2xBvpYK0qVKpcP36daysrCAvLw82mw0lJSXo6+vDzMyMZLwVLbDR80jOEf5P5lysz4WFhSgrK8OHH36IlpYWyfHGYrkX7mbLcRzcbjecTid6e3uxurrKexXMZjMvUCml9ETaL47jeM8bi89O1jotACuh6intd7RlWUq/Uku7knuJ3pMlEpoUqUP4yeo/Xa/w2SLGAKDbLiwslI3DSwbMZjMuXLiACxcuhP0utkaFeOCBB/Doo48iPT0dP/nJT/D7v//7ePPNNxPa382OlHKwRaHRaCISygOBAK5fvw61Wi3KI48GyRSMCYjwGCnInKSlpaGlpSVqWtJWjjkIhUK4efMm/H5/mLUl1nZVKhV+7/d+DwcOHMDMzAzuuece6PV6/qH8s5/9DI888gjS09ORnZ2No0ePoq2tDTU1NZiZmcHRo0cBsK1tp0+fhtlsFhVOWH0Rfue4tfR5fX19qK2tRXZ2NoDwl4iUcJqeno6SkhKUlJQgGAyG5aYn6SgtFgsMBgOzbbF64y0Q02Xp+Yo0VkDuu5JATyXtJIrvT+g2Go0GPp8Pr776Kh5//HGoVCp4PJ6I6lVitaUVA9a8ffGLX0ROTk6YkMmiXUUiiIr1mdSZlZUFo9GI0tJSBINBfs8SsrcC8YrR61eubrr/LNA0JZZ3Rsk+Iqz7ikXpEXrUpPoWzdoSUr2S6c2QokmR+qWuiXCNkWQM9HUnc5qVlYXi4mLxwWwQInm+lJaWhiW/mJiYWDcGYbzCF77wBfzFX/xF7J3c4kgpB1sUkVjsSUrOyspK0Y1KNqIfiYLUC0UMbrcb7e3tfL7lWNvfirQiEl9QUFCAmpqaiPijStslaSSPHz+ODz/8EJmZmfD7/dizZw+6urqwd+9e5Ofno7CwEPX19Thx4gQeffTRMG6+EEoFT1qwIuA4DjMzM5iamkJDQwMyMjLC2mBdSylaj0ql4jnuRMi02+0YHR2Fx+OB0WhEIBCQjMvZKrECSspKXTMhJ5u11mJRdJXeg3V1dfjggw9gsViQk5ODgYEB5OXl8Rs0RdqnSOaYZbE9fPgwgPXKKGv9kntCKOiKxQoopXuRjdZIjIbP5+NjFUgeeTJXOp0upvWoUqkkqSuRXH+WlyuSDFIsRY3lxSCfrDERClAivRmJjjOgaVK08iY8rtVqUVlZuaFxBmJYXV1VtHklsJakoL+/H8PDwygpKcEvfvELPPPMM2HnTE9P897jl156CTt27Ih7n7caUsrBFgUJSJbDxMQEBgYGFKXkjLYfyVYOIvUczMzMoKenB3v27OGtxhvZfjxBuKKRgsRY7Nq1i9/yPhIoFdKdTicmJiZw7tw5fOc738Hf/d3f4fLlyygpKcFzzz2Hxx9/nKdzqFQqXkm4fPkyjh8/LtpuNEJxKBTC8PAwfD4fdu/evc5LIvYilhO4hBSc9PT0sMDQpaUl2O123LhxA2q1GhaLBVarlaf0SdFU5BBLcHIyYgWkBDipuScCmJhSQVuTpWIuqqurcezYMVy+fBl5eXkYHh7Gl770JWaediXzNDU1haeffhqf+cxnkJ+fzwssscwxXZZWFMQUX6l+k3lkKbhCZGZm8sHNoVAIy8vLsNvtuHPnDkKhEE+hEwbmKxkT3Q8asQq5kc51JHx9sWsZCoXCkhPQ9QvXo1gdm0lxIMoO67hKpUJ1dXVMcX3xRCR7HGg0Gvzwhz/E6dOnEQwG8bnPfQ4NDQ341re+hQMHDuD8+fP4p3/6J7z00ku85/fpp59O7AC2AFLKwRaFnFAeDAbD0lEm6qbeDMqBUs8Bx3Ho6emB0+lES0tL3AKqYqX2bHTbJL4g2hgLpe263W6MjIxApVKhqakJq6ur8Pv9+PSnPw2Xy4Vz586hvr6eP5+8PM+ePYtXXnmFqRyQtiNVDPx+P3p6emA2m5lZNuSEuWjaJMqATqfDnj174Pf7eaus2+2GwWDgKUj0WiQWYjGeOxAuaAkVmERZ4BPpxZCyNsspFQCbBibktxMFAwDuu+8+NDc3Y3R0FM8++yxqamr484WfUlCr11Lrvv/++3jhhRfgcrlgNpvx8MMP8/VJlY02biJaIVpqnsTKqlQqGI1GGI1GVFRU8BQkm82G4eFh6HQ63qtAAvOF8S20AB5NjILUmOi6xY4l0vIOSM+plEGB7ClA06CE97uY904O0dKkhPeL8HhJSUlcYhTjBfL8VIqzZ8/i7NmzYb/99V//Nf/9e9/7Hr73ve/FrX8fB6SUgy0KKaHc7Xajo6MDJSUlqKqqSqgbcLMoB3IPcLIDtMViQXNzc1znJNmeA6Vtk/iCQCAQUXyBWLtSL6vV1VUMDg7ya0OlUuHs2bP49a9/jaeeegr5+fnIy8tbZ7manJxEXl4eiouLeSqO8GVJMhvRvFipoN3l5WX09vaisrJSNBe23FijtdALBSWdToeCggIUFBTwgaELCwuYnp5GKBTiBS2j0bhuMyIyRrpNOX4xrVjQCgdddzyts/Q8RINYLMbkvgyF1gJ6hfVkZmaivr4e3/zmN0UVO9ojQc9ZT08POjs7UV5eDrfbjYKCAjz77LN46qmnRA0P0QqrUutbriyB2+2GSqVSlGGL1W+aguTxeOBwODA0NISVlRWYTCbk5OTweyvQdZOxp6Wl8QIxy9sjRmuJZsxSiFVxkIsDkVubdAAyXa9c5iOWIsGiSwnjLqSMB0RRoY9nZ2dHtTlqIpHaHTnxSCkHWxRpaWnw+/3rfp+ZmUF3dzeampriunOhGLZCQLLD4cD169exfft2UW5xLNgKMQderxdtbW0oKiqKS35qqRdrMBhEf3//uvV59uxZfP7zn8dXv/pVphv+3XffRW9vL3Q6HcbGxvDTn/4UTzzxBK/EkJdbMBhcZ4UUsy7Pz89jbGwMO3bsELV80UK8EPGi7rDqzcrK4vsUCATgcDgwMzODgYEBZGRk8F4FIeUlUkFbaA2XC/ZkKRpC4YNWxoT/i81fIilMkXgqIlnvYgGetMDa09MDg8GAbdu24caNG2hoaMDi4iLm5ub4zaFYHipWX+SocnL3uNRcrays4Je//CVu3boFANi/fz8eeughXoGJVkjOzMxEZmYmiouLeQqdw+HAxMQEAPAUOoPBwD+naCU0UnoV/UnWtRiNR2reYlE6yL0kphxstDeDvs+l6JHCftD9pQOSdTodKisrRfuSLKSUg8QjpRxsUWg0Gni9Xv7/UGhtZ9+lpSW0trZuWA7izeI5EOsDodAcPHgwIjdkpO1vZs8BiS9obGxEbm5uXNoVE7Y4juNTfNIoLy9HcXExrly5wu8KS2Cz2dDf34+CggKMjY3BaDTinXfewdmzZ1FeXh4xLYXj1tL2ulwu7NmzR1SBFFs75EXJ8lLQ5eVc/3RZ1lg0Gg3y8vJQUFCAYDAIt9sNh8OB3t5eBAIBfhO27Oxsyb7EMwaBtjiKWThZXgya486aBxbtRPh/tAIUXTYShSUShSQnJwc+nw+lpaUwmUy8d0L4nGGNiRWcLkcHIpQiVuyFULlljfeFF17AjRs3eOvv1atXkZWVhfPnzzPPj2Y+1Go1zGYzzGYzKisreQrd1NQUlpaWeGWXjnuIVtFlrQ/W+qT7yvrOakfYhtj9Gwqt31FYeDwaKKHuxUuxoO/XQCAQ9pxUq9WoqqpK6ganYnC73SnlIMGIblvcFJIOoVDu8Xhw5coVaLVaHD58eEM3J9kMygFL8AsGg+js7ITNZkNra2vCFANgc6cyHRkZwa1bt3D48OG4KQYES0tLuHbtGtra2uByuQAAY2NjWFpaYp6vVqtx9uxZvPrqq+uOud1u/vuvf/1r1NbWYnR0FHNzc2FjlLNEA2tW+Nu3byMYDPKKAQtSc0euKREUiDDA+iPnCGk/QqWCWBfVavU6DjwRloR8cpVqLd1kWVkZmpqa0NTUBLPZjIWFBbS3t+PWrVuYnJwMS7+ZSFpPNBZQMiaxOQQQRvURU6qEQjH5o+eQ9nBIKWjRjodVdu/evdDr9ZifnwewttnS/v37YbFYRMsuLS3hwoULYUkEpNol7ZFnrJAiJbUGheXb2tpQUFCAiYkJzM7OIjc3F9euXWOuwVjmQwitVouCggLU19dj//79qKqq4mmDc3NzGBgYwNzcnGgyBaUe0UjK0kK/2B99LoHwXhZa2uk5lDIoxDIu0i8xxKo40P0tKyvbtAI4yaSVQuKQ8hxsURChfH5+Hrdu3Yo660w8+rG6urrh7QpBW39XVlbQ1taG8vJyVFRUxEyhibT9jYTYyyYYDOLmzZsIhUJobW2Nu/VnbGwML730EqqqqgAAv/3tb3Hq1Kl1Lx8y90SBu//++/GjH/0IHo+Hf7irVKowgerLX/4yACA/Px+9vb3Ys2fPOmqRsH7h/x6PB3fu3EFJSQlPd2Ah2gBZueMsy5xQaJNaJ2KWTuEmVsDa+rbb7RgcHITP5wvLIMPKwBQLrSeaTFhy9UYqxAj7r+ReY3HBCWeePkZThpT2CVjjYj/55JO8EaK+vp6ZAlFY1mg0Ijc3F1evXhXd+EyuXXpccspOeno6AoEAQqEQBgcHYTab+axKckojTeVh9Y/lOaNjNgwGAwwGAzIyMrC4uAiLxcKn/E1LS+PjbbKysmRpohtN2aHHxlLY5PrFcR8FIIspDixPhdSzTqx/LEQ6L1arNe7GpHgiRStKPFLKwRaFWq2GzWaDy+XCkSNHmKn4NqofyY45EAoMs7OzfMwFy4KXqPajFaLi0TY9/x6PB21tbQkNSH/99deh1+tRVFSE1dVV2Gw2vPLKKzhz5kzYecSKRubHbDZj//79uHTpEh544AH+pWUymXDo0CFcvXoVwNqLt66uDs8//zz8fj9qa2tx+PBhnhNLLHXCFyIRmOvq6pCdnZ0wS3q0HPlIBR4hx11YNiMjA8XFxbzy43Q6YbfbMTw8DK1WyweNEuVLLmhSLFYgXnz/SBAPpYLuGxmjXICnUKkTzhntdRDeT2azGffdd19EfT5x4gQuXbqElpYWxeNlzbXSgNnjx4/j5ZdfhtlsRnt7OxYWFvD4449HdH0jEVLJ85j26BCQHcfJ3iA+nw92ux3j4+Nwu93IysqCxWKBxWJZl8teiedQakzxVBzotSAFWqmlx6AkAFmoONDxFULI0Rxp0POSmZmJ8vJy2XLJREo5SDxSysEWhM/n42kTd999t+TLP9HYLLQin8+H3t5e2Gw2HDlyRPEGKfFAMj0H9IPdZrPhxo0bcY0voMFxHGZnZ6HX6/HCCy/A5/OhubkZDoeD2T/6BXXu3Dk899xzeOCBB8J+3717NyorK+F0OjEyMgKO43D58mVkZmair68ParUaZWVl/FwLs31MTk5iYWEBjY2NyMzMZL5Ihf0Xsx5HK/wnSiCWEx7VanVYBhmv18tnkPF6vWEZZIReBSX9pSlRwt9p2oWYIsOqc6OVChbdRqqssI9y3HapWAEhH19Ydt++ffjJT36C/Px8NDY24tChQ7Kppul6IvEo3HfffcjKysLly5f5Ng8ePChaNh7XgV4XtBdNqPQQChKJiSB7K/T09CAYDPKKgjDehmVdj+U5HI3iEAqFwu6PRMUZiHkjlZYXvqPFnonkXtdoNKiurk6qTKEEkaYyTSFypJSDLQYSXFpVVYW5ubmk38SbQTkIhUIYGxtDcXExjhw5knAaEY1kek+E3PiRkRFMTEygubmZma4wXlCpVKiqqsJ7772HAwcO4O///u9RW1uLsrIyReXvvvtufOc738Hc3BxPlSEwmUwwmUy4cuUKioqKsGPHDty+fRuHDh1CX18fSktLw+Y7FAqhv78fHMehsbExLAWo2ItUTFikqRDCMmKCHvmMlpsd71gBsoFVSUkJAoEAFhcX+b0V1Oq1fRdyc3Oh1+tF7xOhYCnkuJP+illAacFDqn5SVlg+UUqF1PMgkQoJ+aS9W88//zzS09PR09ODsbExDA0N4bOf/WzYvNHrTRh7wRqblGVfrVajubkZzc3N2LZtG65cuSJJE0okpUdJhh+Sxau8vByBQAAulwsLCwsYGBiATqfjs3gJ17CYYkDHotD3L0sRVBp7QeqLhaokh3h4O1j3K4v+FQqFUF5enjQWQiRYWVlJyKauKXyElHKwRcBxHIaGhjA1NYXDhw9DrVZjeno62d1KunLgcrnQ29uL7Oxs7Ny5Myl92AzKQVdXFwCgpaVlQ7JLnD59Gu+//z4WFhag0+ngdDrx4IMPhp0jJkikp6fjxIkTeO211/D444+vO65Wq6HVannPWCAQQDAYhFarDXvZ+Xw+dHd3Izc3FyUlJbJKYSQWerrfkQpMtKAntMKT+uUErVhiBYhVMzs7G9nZ2aiqqoLP54PT6eQ3YSP0jZycHN5yHat3RIzSEEmMh5R1U64dVp8TwU+PtmxHRwf8fj/q6uowOzuL1tZW9Pb2Ym5uLmyncFrBpfntBPTYCF9fbA6PHTuG73//+/D5fLwQqNTrEy9FinWfitVNKEi5ubngOA5erxd2ux0jIyPweDzIysqC1Wpdt7cCAe0NZFH3aAWBQIwWJSwj5imRG5fS41JQ4qWLxCNBPDRbASsrKygqKkp2Nz7WSCkHWwB+vx+dnZ3IyMjghT+/3590iz2QXOVgbGwMw8PDqK+vx+LiYlL6ACRXOVhdXcX8/Dy2b9+OysrKDfOaWK1W7N+/H1arFS0tLaisrFxHWxHSTuh+ffnLX0ZmZmaY8CZ82e7evRtvv/02srOzAaztV0C8Qhy3lvWlt7cX1dXVPKUmWutyIoKThWMhlneauiLVplAwYYFF6ZGrNz09HYWFhfwmbEtLS7Db7Xz+e6vVCrPZDJPJpNh6ShBPypVSmhfpl5xioVKpwjbeYrXFqleOzy/VJ7GyS0tL0Gg0qKysxI0bN3ilkaT+jdVyTz+LaQXNbDZj586deO+993Dfffcx6xabQ6HlnVbOlCpSLMt8JAI0HW9DKEhkb4Xs7GxYLBaYTKaYrfosz6PwmJBWxDpHOJ+se5mlLClVqJUgkjWq1+s33UZnUkilMk08UsrBJofL5UJnZydqa2tRUlLC/67RaDaFcpAMwTgYDOLWrVsIBAJobW3F4uIinE7nhvZBiGQpBwsLC7h+/TqysrL4rEEbheHhYfj9fn6zJyFY80G7sYnQLyYw19bWQqPR4Pbt2wiFQrj33ntRV1eH6elpOJ1OzM7OYteuXcjMzORfrtEK/4mOFWAJsNEKl3JjYX3SQYukfaIIVFZWIhAIwG63Y3p6Gv39/dDr9XysghwSYWFXUpY1jywrOFHMxOIKhL+RPgnrousXlo3UUtzQ0IBr167BbDajpaUFS0tLvNImNV6O+2jfDTEo9TQ98sgjzKxWYnS8SK4hvc6E5YUeNOF5JHhZrm7WMXoNOxwOzM7OYmBgAJmZmfz+INHsCi13nL6vhKDXl9hakxqbmGJBlDGptSj3jBFCo9GgoqKCGTO2WZFKZZp4pJSDTQqO4zA2NoaRkRHs378fRqMx7HgkN38isdGeA1YmnmQGBAMbrxxwHIfh4WE+r3pPT8+GtQ2s5XMXe5HESxDnOA6VlZWo/L/dOYlVdG5uDl6vF3v37oVGo+FfkLTgJ+wPzTUWthEttSfScSq9V2OdPzGBRM5TodFowoJC3W43bDYbent7sbKygqGhIeTk5MBsNocpHYni7MdCq4pWISHrQWlWIxqsVKk06uvrcfLkSbz11lvgOA5GoxH9/f24ffs29u/fL1qO9I+FYDCInp4e9PX1IS8vD3v37g0TnOj5uPfeexWPSQ5SdDwyF8LEAcFgkL9vSd/EFApWnICwDXpcZCPBvLw8noJks9kwMDDAp/wlgc1arTZmLn8gEIg65i8S4wBLAZVao3QAMm0koJW5qv/b6CzZ8YuRIJWtKPFIKQebEIFAADdu3AAAtLa2Mndh3CzYSOWA7OnQ1NTEU0mA5KdT3cj2g8Egrl+/DrVajZaWFgSDwQ0d+8LCAmZmZpjH5ATQaOg5wNr8rq6uoqenByqVCgUFBfw9IeWlkBP0xPorxjUW1i+mWEhZpMX6q+RYLMKy0vUprF+v10Ov16OsrAxtbW0wGo2YnZ1Ff38/v9ut1WoNywomNmditIlEKBViEHoFEtUuoZDJlT127Biam5vhdrthsVjwn//5n7h48SL279/PFOaEdbCoZM899xwuX74Mv98Pg8GAy5cv40/+5E94BSHadQPEHoDMujeF60TM8wNIrw+xfguvM9lboaysDKFQCIuLi3zKVLVazSsKRqNxnYKipG0xz0EscyoHJX2jA5BpI4Ew7XZhYSFMJhNWVlY25U7IYkgpB4nH5pU6f0extLSEjo4OVFZWory8XJJ3vBmwEcoBx3Ho7+/need0NgW5TXMSjY1SDoSbuxGLOk2XSCT+8R//EZcvX8apU6dQU1PDW5rIyy7aF56cYLu8vIzu7m6Ul5fzFkHSbrS88Ggtz0qUHOEn+S60zLEEvEQFJkZDzRH2iVA+cnNz+aBQj8cDu92Ovr4++Hw+nrphNpvDrOeRzKHYvNGQW2diAidtMVVaVnhMqcA4OTkJp9OJkpISWCwWZtnMzEye6nLq1Ck8+eST+PrXv74ugJp8py3uBPPz8/jwww9hNpvxzjvv4MKFC5ienkZnZyfuueeesDqE31keN7ExRQOxugm9KFHrXWztqVQqmM1mmM1mPsbD4XBgamoKy8vLPI3OYrGEURXF2hbzasRKVdrIAGWTyYTi4mIAa+trKykHqVSmiUdKOdhEmJycRH9/P/bu3btl0nQlWjD2+/3o6OhAVlYWjhw5wnR9JptWtBHKycLCAm7evJk0r8nt27dx5coVXLx4EcXFxbh+/TpKS0v5lwqLV09/Z3Fn5YTThYUFDA0NYfv27cjKysL8/LxsOdJWNJSgeFnvaYGMBDBK1StleWeNORohXKy/So+pVCro9XoYDAb++rtcLtjtdgwNDUGn0yE3NxfZ2dmSQhYNJfx2sfHQ80a3SQJTpdZNPOYxGAzi5z//Odrb2/nn1Cc+8QkcPXpUsmx5eTnMZjMuXbqEgwcPhmWMkVNYbIuAmAEAACAASURBVDYb0tLSkJ2dDYPBgOXlZWi1WszMzEiuOboe1nfSPwKhYhHtfJHYiWQJyKRunU7H0+g4joPb7Ybdbkdvby/8fj+/6zhReFljC4VCYfMjpjCw+ghsbGYjGjqdLixOTSrF7GZEynOQeKSUg02AYDCI27dvw+v1orW1VXZDHCGkgqI2Aolse3FxER0dHairq+MtHCwk23MQCZc+UnDcWgrb6elp5v4FtKUxEfD7/Xj22WdRWVmJjIwMeDweWK1W9PT04MSJE5L0gGgFUGAtG5XdbseePXug0+kAgFdEyHmRCnrJCE6WozcB0ilAxcoK+8sSkOlnQzT1siAca1paWtgmbD6fDzabTXQTtmiVNinICavEoi/VrhKhjrQl1ufu7m60tbXxwcWBQAAvvPACGhsbmYHdZJ4nJiag0+nw4x//GG+++Sb27t2LT37yk9DpdGHKJi3EcxzHp/BdXV3FiRMnEAqF4HK5UFdXp9hLQq+9SJVgWkAWWtfpeZN7X8UjSFgMUjTCrKwsmEwmhEIhfm8FovCSXcetVuu6BAgsg4eYAis3p8Jnpti4pO5npfOmUqlQXV0dRlcOhUJbynOQUg4Sj5RykGSsrKygvb0dxcXFaGxsjEjYJkLxVrqplWJiYgIDAwPMYGwaH1fPQTAYRFdXFzQaDVpaWpgvjVj4q0oQCoUwMDCAhYUF5ObmYv/+/Zibm0NZWRncbndCLPTBYBC9vb1IS0vDrl27ws4lNKpoBT0ivCiJFYjHWOTu52jnj+VFEH7K9Vd4vwgVClqpIN+F45DqU3p6eliqScLzHhsbg0aj4SlIBoMhKp63WLvxsDRHo2iSOlQqFQYHB6HT6eD1enH58mWcPHkSKpUKU1NTvDeAvmbBYBD//d//jaKiIrz//vs4evQo2traUFFRgebm5rBzWWvJaDTi4Ycfxv/8z//w/Tx48CAaGhpExxzPuAuWx1AYgExDKh6HfGfdu8RKHwstTOn9TfZWsFqtANZ2HXe5XBgeHub3VrBYLGHW9nh6O1iUKCXKLW0gYCmUAFBaWrqOkrMVaUUp5SCxSCkHScb09DQaGhrCqCJKQfj+W+mmlkMoFMKtW7fg8/kUe1E+jgHJJL6goqICFRUVca07EgwPD2NlZQVVVVUYHR3FkSNHAKzRnIqKikTXn9ic+P1+rK6uiu7Q6/V60dPTg/z8fKa3SCqdoxitB1CmRMnReoTWPSVCuFzb8QgijrQsS5CWoosQoUSKyy38LvxfrVaHeRVI9pixsTGsrKwgKyuLPy6VdCFWyk88BEYWhAIbx3HIz8/H6uoqrFYr/H4/7HY7gsEgLBaLqFBss9ngcrlQWloKnU4Hm80Gs9mMmzdvoqWlJawdofAs7NfBgwdRX1+PyclJZGdnS24OFYtlPtYYBXKcRVWivyutWzgnLAVKaHGPNp5Er9cjIyNj3f4gXq8XnZ2dYfuDiNFeY3k/ROoNoZU14XGLxbJuV3pg69GKPq5G0c2ElHKQZNTU1ERdNtm7E8cbHo8H7e3tKCwsjMiLshHUGrn246kciGVl2mhMTExgcXERarUahw8fhsvlwuzsLAAgJycHpaWloi501nx0dnbyWVVycnJw9uzZsBeVy+XCwMAAampqmDQMcp0jFbTlwBKIhcdiofWwjinhbEcrhG2kUgFERh/T6XQoKipCUVFRmJA1OTkJlUrFKwp09hglVJdIxxNrWVZ/9u7di3fffRfT09PIyclBT08PPv3pT6OwsFC0bqIkB4NB3HPPPTAYDHA6ncjJyVm3JlWqjwJ5aaWM7IRNQ2mcgJIxS0Hpmo1GUZOqm4wrmvSzcrEqpH7h+lOpVDCZTDCZTFhYWEBTUxMcDgfm5uYwMDCAjIwMfqdhvV4f85zH4hmm5y0jI0PU0PRxMzKmEDtSysEWRlpaWlhasq0MEnDb2NiI3NzcZHcnIsQr5oDjOAwODmJmZoaZlWkjMTc3xysCwJoQc/78edjtdqhUKlgsFty5c4fJwWZRUcbGxvDb3/6WT0PqdDrxq1/9Cp/73Of4AEriRWONWygUsayw0b5g4yVoy3kUhEoNi5pBf0rFcPx/9r48uo3rPvcbACQBEiAAguAKUly1UtS+0rJjR5v3JcriOM3S1M3LiZt0eWmSvtZx0uTk5Lw27jtNmrpNc9qkdhzLii1b3lrvijdZlKiNFCnuqwgSJAiAJIht3h/wHV0M7yzYCFLFd44OKMzM3XBn5vf9ft/v3kRzBdKh91e6Vk7nXVhYCIvFgkgkgmAwiOnpaQwPDwurx9hsNlgslpjlUunr6YgO67gcqUgHOdPr9fj617+Oc+fOoa2tDc888ww+9alPLYqm0NeShRbefvttgRhoNBq0tLTI1svyuMejx5cyiKW8+kpjkmiOgpp2yyEZIi0mTPHmCmg0Guh0OpSUlAhOjrm5OUxPT6O3txcLCwtCzo3ZbF4UHUuWOMQzbhqNBnV1dZIEIOuJz0KMLDlYwVgukQPygE4kLEkbxKyE25WAePJEpBAKhdDW1oacnBzJ/IKlwszMDIaHhxd9r9FohA2GAGkjlpXo2NXVhby8PMzOzqKtrQ033XQTrl69ivHxcfj9fgSDQTQ3NwtJq2IQr2m845Ku5OR4DW16zORkPXL1SuUKkL+l2qTkXV0OpCInJ0cwsnj+2uoxHR0diEQiQq4CkW4o5Qqw+kDXyyKw4vNZ81ipvwaDAbt27cK2bdvw+OOPo6OjA01NTUKZrGtvv/12VFVV4dKlSzCZTNi9e/ci6YfSGMfrgRbPuXikK3KednH54raLox7LIZohd73cuNCSOwK9Xh8THZuZmcH09DQGBgag0WhgsViE/RXk5iBNbkld8bRdfLy6ulr23brSZEVZpB9ZcrCCsVzIAWlHvA+XYDCItrY26PX6jBvEmcTs7CxaW1sznl8AQNgNV63BJZecSCM/Px/hcBgWiwUXLlzA1q1bEQqFBBlRfX09M/GOZdSwjou97nKGs5IRroR4CUc88rh4yhWPtVpSQbdJjlSQOhLVaidKKjiOg8lkgtFoRHV1NUKhENxutyDdyM/PF8gCK8okZQiz6o3H6CL9VTKOOY5DTk4O8vPz8etf/xo//vGPFcdi69at2Lx5M/O4EpI1guUgN+/USJVYOQCE3MnlC5A6litxUJKykr4QuVdtbS0CgQCmp6dx9epVXLlyBQaDQdhbgZ7Hau8rKWIhljPSydVSCIfDca2SmElkUkL8PwlZcrCCsdzIQTwPF7LZW319PRwORxpbt7zhdDpx6dIlbN68OWZ980wgEAigu7tbdfIn/X8lw3bt2rU4deoUZmZmUFtbi3fffRcbN27Exo0bFV9cUm1gSQKkPPRS7ZYjESxjRe7FraSNTsZYTnUOgpRnV821tFEiR3wSlYGJ69XpdMImbECUTE9PT6OrqwuBQCBmE7acnBzZNidjEIrnmFJE4dChQ3jmmWckySr9f1puw5KoicsQX5ton5YiAZmG3BjKOQXo78V1iMEqOx6ko98AhL0VyEIOZB6TvRVIVMFqtco6yqTGjLSdJvRkl3MlhMPhjMpY48HCwsKKaetKRpYcrGDodLplQQ7i9eCMjo6iq6sLW7duRWFhYRpbtnzB8zy6u7vhdDoznl8ARF8O3d3dCIVCTI8US8NNjBY1xqnFYsH999+PU6dOYWJiAu+99x5+8pOfyCZcSxmWSnXGExUQv2jjMbRZhgpLZsVxnOpVluJFJhKblYwvNTpu+pNVtpScguM4FBQUCJuw0WvS9/f3IycnB1arFUVFRcJSh2qMxGQkJlLj/JnPfAbHjx9fJKWhjTe1vxHtKWbdm3TZ5DNeuVA8SHRuEflpPPkR4u+VkpuVSK2S111u7Ei/E72X6dwpo9EIo9GIqqoqYTNBt9uN/v5+6HQ6YR7Ty/4q/aY0tFot6urqVEXkV1LOQXZ35KVBlhysYCy3yIESIpEI2tvbMTs7G/dmb2og5V1bbiD5Bbm5uZK7Pi8leD660dr8/HzMdwRq9OpiTyj5pD2iBQUFsFgsuOmmm3Dq1Cm4XC5JcqD0glcb3YjneLyGttjTKTdGSrIe1hwghlSmSUUi0hsp0MdZ5crJmMh+IvRY5ebmwm63o7i4GBzHYW5uTti8iiSEBgKBpORRSv2VKre8vBy1tbU4deqUsARwPGCNFd0PNb+/mGypIRbiuuOFUruU9oVJhIipqZs2+uXuKfFx+hlG1yHOgVJLLFjQarUoLi6OWfbX7XbHLPtLlkwlG0Iq9b2mpoaZzM/CSso5yG6AtjTIkoMVjJVEDvx+P1pbW2G327Fhw4aUG/ErZUO42dlZnD59GrW1taiurk5JmSydfTwYHByEx+NhHlPyLrM2PKINEvL35cuX8cQTT4DjoqvUNDY24rnnnsNf/MVfCOdKkQq6TDmiooRkkpMTlW5IGbypkvVIySoSJUFKSNc4qTH6pDbXog0+vV7P3ISto6MDOTk5sNlsMd5Y2ovMmsPJjtXHP/5xvPrqq0xyEM9Yiu/vdCYgS0XIxM8ZqYiFUkQgGRmUHNIlBxJHK3meRygUYo6TFCmIV4an1+tRVlaGsrIy8Hw0Qd/lcmFkZESIxNIJ+uK2lJaWMpe2lcJKWso0Sw6WBllysIKh1WoRDAYz3QxFcuByuXD+/Hk0NTXBbrenpQ3EeMjkA07JQCf5BVu2bInrwa0E8mJIpO9Xr17F5OSkbLkssAwq8XFybGZmBv/5n/+JsrIyIb/A7XbjxRdfxJ/+6Z8KkhvyApbzwAOLvaFyf5PzE80VUEI8Cays44ka8MnIhcTESwwpAzJdpCJd12o0GoEINDQ0AIjOO3qn2+LiYlgsFuYmbOLfj5UnIP4biJ1v+/fvxwMPPIDvfOc7MXUk0ie6HUuZqEsb/vGSEnGELBKJQKfTMYk/sLwTkMXRNLVkTU0OhJSMDojKh8neCrW1tQiFQpiensbk5CR6e3uRm5srLPtrMBhgMplQWVkpWRcLK8GxRpDdHXlpkCUHKxharRZ+vz/TzZAkBzzPo6+vDyMjI2lfplQpVJ1uyHnv6fyCvXv3qg71qkW85GB0dBSnTp3C9PQ0rFYrM2FNrcHMepnRL0q3240PPvgAJpMJxcXFOHr0KPbt24fKykoUFBTgww8/xO7duxOqU60MgvXipr2BUka6EqmI1/Or9tqlkAsp/W6sa8kna46LDel4JCrpypsQX0t7YyORiOCNHRoaAsdxgjfWZDLFyLlY803tb1ReXo6qqip8+OGHi/YukIpYsJ6nZGyTic4oHU9H2ayIBSu6wKpbbHxLkVql+1QJ8UjhCGgZTjJjrua4OMdBo9HErEBEdh7v6elBMBjEpk2bMDY2Brvdrlq6u9JkRdmcg/QjSw5WMJaLrIj1cAuFQjh37hx0Oh327t2bdq9EMnKTVNUv1kMD0XE4e/Ys9Hp92vIL4nkx9vX14Wc/+5mQADc/P49Dhw6hublZKIsuV+xFpl/w5IVN95ueCyMjI3A6ndi+fTva29sRDodRUVGBS5cuYf369bjhhhvwwgsvYPfu3apzBeL1aEuNjRoZhJKsRypXgCaJLMKYiSRiJSjVS8tBWOMvF+1RI6mgj0t55MVINKkViHpjTSYTTCYTampqhGUmR0dH4fV6YTQahYRQscY7HmOP53ns379fkBapIY1kLMWEjBBZKTnPUkcU4imbHJeLpIlBz4N4d0BmRRLl6pWbK3KOg3RJmeI5rtfrUVlZCYfDgfr6eoRCITidTvT09AAA7HY7SkpKYLVaJccg01H3eJCVFS0NsuRgBWO5rFYkJik+nw+tra0p1dWraUMmIweshzgZh7q6OlXLyaWybim89NJLyMvLg8/nE5Lg3nnnHWzYsEEw9uUMGDFRCIfD+OQnP4l//dd/jdkgrbu7G+FwGJs3b4ZGo8Hu3bvx7rvvorS0FC+++CJ27dqFW2+9FX/3d3+nKMei+ydO0E1nrkA6ZD10Ui2r33KGcaZIhdrfRgpS0QqWVENcp5Jhx/Lwk/OlyAxrrMgyk6WlpeA4TshVaG9vRyQSEZaYNJvNcY8zkRZ9+9vflkwmBYDx8XG89NJLGBwcxNq1a3Ho0CGYzeYYAq72PpcaN5acR00eglJd8ZAlMaFOB2lRmzOiRCzEzxu6fCVHTyIRCaW2yR0vLy+H2WwGACGqEAgEMDExgYGBAZw7dw5Go1EgC7SBvZJkRVlysDTIkoMVjOUSOaDbMTY2hs7OTmzZskV4UC0FMh05EJOT8fFxdHR0YPPmzSnNL2BB6gXGgtPpxPz8PLq6unDmzBns27cPer0eoVAIwWAQY2Nj0Ol0qKysXBSSZiXgcRyHjRs34uWXX8ZnP/tZBAIBtLe3o7i4GJWVlcKLds+ePaiqqsLg4CAuXLiAmpoaOBwO/MM//EOMxIcFubyGdMtvUlEuHfUQJ9WqNWiVSAW5Jh2kItHxT6Ze8XGpcZKrlzaQSdKmWP4nHm9yLYkqrFq1StB4k03YpDavkupvWVkZqqqq0NraKkjoxJiZmcFPfvITLCwswGg04uTJk+js7IzJVYhH6x+P4S+XgCyuQ1y++G+lsuPR6rP6JYZStDGR+UnPBal3CjGm1Uih4m23mraLj5vNZpSXly86Lzc3F5WVlaisrATP8/D5fHA6nTh37hwWFhZgs9lQUlKCUCi0YshBdinTpUGWHKxgaLVahEKhTDdDaEd7ezs8Hg/27t0r6yFLB5LxPqUC5GHN8zy6urrgcrmwZ8+elOcXsKC27zzPo7S0FFeuXEFjYyNeffVVvPvuu/jCF74Ap9OJZ599FqFQCDzPw2q14siRIzAajZJ1kBf3HXfcgb//+7/HgQMH0N/fj/r6euYSpQ6HAw6HA4WFhbBarYsSHNUYtbT2mP6Ukx3FM17pjDYkWm4ypEJMJpRkY/Ho6tMl+UlVzgWpg9yXhDBI1S0mFUB0jEhUgc5VmJqaEjZhs1qtsNlswsoxLBw4cAAvv/wyNm7ciPz8/EWGd1tbG2ZnZ2E0GtHZ2YlNmzbB6XTiypUrWL9+vawcJ9Wed3ouxBtVEs8zMeknBE1cFwvLkTiIy5CqU8lZJdV2UqaSw4c+lpubi5qaGtm2krIJ6a2vr0c4HIbL5cLExATcbjdOnTqFkpISlJSUoLCwULX8a6mRjRwsDbLkYAVjuUQOwuEw+vr6UFVVhV27dmXkoZJpWZFWq0UgEMDFixeRn5+P3bt3L1mCl1pPd39/P5qbmzEwMIChoSFUVFRgeHgYW7ZswSuvvAKDwYCCggJEIhFMTEzg9OnT+NjHPiZZPnnBlZaWYmRkBD/4wQ/Q1NSEkpISgRywXrJNTU2Sx9T0iejfWTp4OYOGRDpovbC4XHIe/X+CpYw20OUmQyqkDD+lssXjJJ7L5HgipEKNgZ7ItXK/AemDmrFiecVpYy8/Px/5+fkxm7BNTEygp6cHubm5KCoqgs1mEwyYSCQCvV6Pl19+GbOzs2hoaMCnPvUpFBUVCfN1fn4eHMfBYDDEtJHeo4H1XE1Ws56Mcc46zopY0HUQosb6HcU5FqQOVvlqPOvplEmRpUyljif6m5D5oJZYcByH+vp65mpbStBqtQIZmJiYwNatWzExMYHu7m54PB4UFhaipKQEdrs945t00pibm4PVas10M657ZMnBCsZyIAfT09Po6elBcXEx1qxZk7F2ZFpWFA6HcebMGaxevRoOh2NJ61YjKxodHcXU1BT0ej0++clPwuVyYcOGDfjRj36Ed955Bz6fD2VlZXjllVdQUVGBhoYGDA4OxrywWS/z2dlZPPnkk6iurkYgEIBer8cLL7yAz33uc7BYLAl52ZUMwGSMSympilK9SpEKOW+o3O+TKi+5GMmSCrGBTJ+rlICsFKkQ/0284snKlOQkHOkaZ51OB7vdLmi85+fnMTU1he7ubvj9fpjNZoyMjODdd98VdoMfHBzEr371K3z9618XnBpNTU144YUXEAqFsHXrVvh8PuTk5GD16tWCt532upMxToYYJEq01JSdyHiLSYTassVzjHVPkvLJd8lGWqQiOekeN/HxqqqqlHnRDQYDqqurUV1dDZ7nMTMzA6fTidbWVoRCIRQXFwuOn0xKkGZnZ+NeqjWL+LEy1q7KgolMkgOejy5TeuHCBaxZsyaty5SqQSYjB1evXsXU1FRGiAGg/EJxuVwYGxuL+c5ms2H//v3QaDR49tlnodfrMT8/j9raWly8eBFer1fQsIq9f8C1l/C5c+cQCoWwb98+tLe3Q6/XIxwOY2xsTNLbmYyXXW7OJ2sAKhnwxEgWfwLXPKLiMuiXKNG90/p3IHb1o3jblGhf03ktHdUhhhQ9XvT/xUSCjlSI/5H66XPVQA1RSpWRbDAYUFlZiaamJmzZsgXFxcU4deoUAoEA7HY7enp6UFhYiLGxMUxNTQnXOhwOfO5zn8PCwgLGx8eh0+nw1a9+VYgk0OMlJUcRjxtpHz3fpMg+z/Oq98yJVw/PGrNUevXF4xIOh2PmGT1+QGyCPGvOseafOHoWiSxemS6RtsdzXDzXioqK0rZvEMdFl/ZdvXo1Wlpa0NLSApvNhrGxMZw8eRLvv/8+enp64PV6E/4tE0V2KdOlQTZysIKRKXIQDodx7tw5cByHlpYWTE1Nwev1Lnk7aGQickDyC6amplBWVpYxHaTcS8Xr9WJgYIB5TKfT4fDhw3jmmWfQ398Pr9eLsrIyOJ1OBAIB7Ny5U/LBPz8/j+HhYZhMJlgsFthsNtxyyy0Ih8PgOI6ZrMfzvPA9Sy5Ae49ZBh0J58c7BuR4IoZ2Mp5Aek6Kve9KZbNyBegxoqMYwDXve7L9SZfkR821UlEdVrksGRMrWkGXQY8XLRdKF1HKycmB1WpFRUUFvF4vSkpK4HQ64fF44HK50N/fj0gkuhKSTqfDrl27sG3bNvh8vkWLGIiJNsu4p89TGzXiOA6nT5/Gr3/9a7hcLtTU1ODBBx9ETU0NU16nZAgmE7FSc1yp7ngjDuJ5pnZ+s6JjUvNPrfEsd564bXq9HqtWrVJVbiqg0+mEPUKAqIHudDrR0dGB2dlZWK1W2O122O32tOcbZnMOlgZZcrCCkYwHJlHMzs6itbUVq1atEh5Oy0HelMxLJREEg0GcOXMGRqMRu3btEtbxzwSk+u73+9HT0yM5R4LBIHJzc8HzPKanp7Fp0yZMTk5i7969KCgokFxtyu12o7u7G6WlpQCA4eFhTExMoKGhAdPT04IeWwxagyzl/ZTaTI+QCuKJZ2ngCTGJJ1cgnbKeZCRMarTc4vLE5UrlCYiNnET6o6bNqbpWrbHJ6hNdt7gOqQRkpTbEK+lpaWnBhQsXoNVqUVFRAZfLhY997GOor6/H9PQ0hoaGoNFohH0VWKub0cZoKg3owcFB/OM//iMMBgPsdjvGxsbwox/9CI8++ihTZy4mFvQnXQcBTfQzIVWi25RKrz0dOVAjW1OSQkmB9azUaDSor69fspw2FvLz81FTU4OamhpEIhG43W44nU709vYCuLa3gsViSXk7s+RgaZAlB1moBlmec9OmTTEJQUttmLOwlLIir9eL1tZWNDY2CtrHTBA1AlbdoVAIPT09skbx6OgocnNzYbFYcPHiRezfvx88z2PLli24fPnyomt4nsfo6CgmJibQ3NyMqakphEIh3HvvvWhtbcXQ0BAaGxuxY8cORcMi0WO0NIWAfrFL6f1ZMhRa/y7+jnyfaLRBXE4816bKO8+KVChdyzL4aKM0XlKhhHReq1ZTz/KMq22X1HjR0bG6ujo8+OCDePXVV+HxeHDrrbdi3759wr1XW1uLQCCAqakpjIyMwOfzoaCgQFgulRB4InFJpQH9wQcfgOd55OTkYGhoCNXV1XC5XGhvb8fWrVtlyxbPBanxZhFa1riJI4p0+ekkDnRdLEhJmWjpVrxtiydiIb5+1apVyypBWKPRoKioCEVFRVi7di0CgQAmJycxODiIc+fOoaCgQEh8ToVRn13KdGmQJQdZKILneXR2dmJ6epq5POdyiRyo1cwmA6l9HDIha6LrFhuFJCFS7nxiMN922224fPkyQqEQOI5DTU0N7rjjjpgXejgcxpUrV6DRaNDc3CzocHmeR2FhIW6++eaEjel4XuziF2k85bK87VLX0mRTygMvJethtVmN0ZmMJCNZ+ZOS910q2qNG0kOXQZedqWiEEuIhHWr71NDQgIaGBslohV6vR0VFBSorKxGJRODz+TA5OSlswhZYWIDX64XZbJb0xCZClsgqN1qtFoODg0I0UJxwmmrjXCoSJhVRZHndWaSbVX4yJFIK9PMzlREJpeN2u525THQykHt2JYLc3FxUVFSgoqICPH9tb4Xz58/D7/ejqKgIJSUlKC4uTmiVpWzkYGmQJQdZyCIQCKC1tRUWiwW7d+9mPkSWAznQarVYWFhIW/k0QWLt45DJ6In4BdTf34/Z2VnmuXQ7S0tLYTAYkJubi/3798Pn80Gj0Qi7WpMXpt/vR3t7O8rKymI2NiMGBJH80NKHdGng6fmXDg98JBKB3++HwWCI6YtSucRQEBMv8THSbjWkgsZyJBUs77vaiII4p4KUx6qDhhojLlURhUTKVtsuqWhF2O8HhoZQ0NuLgr4+rDp/HnxbG8KRCLr/7d/Q3d2NgoICYW8F4kEWRyvU5lbs3r0bzz33HLxeL4qKitDf34+GhgasW7cuZWOSrBxIKt9ETX4F3Xa5uUb+L/5dpNpOy4oSRbzEIj8/H1VVVUnVyUIkkr7dkTlu8d4KU1NTcDqd6OrqglarFSRIZrNZ1bNwOZGDW265BVNTUwCAy5cv49e//jU++clPZrhVqUGWHFwHEL9kUwW32422tjasXbtWSERiYTmQg3R67kl+gclkkiRImSQHtLE5PDyM6elpyfPoNubm5uKuu+7CyZMnMTIyguLiYtxyyy3weDyYmJhAZWUlhBsv+gAAIABJREFUFhYW0NXVhcbGRlgslhgPMs/zCIfDgtSHhlgDLyUjIIZzIsZlqo3lQCCAjo4OaDQaYadam80mJIwqgeNicybEfVJLKug+sKIO8Xg6l6vkhxWJUCvpIfc6Mc6kJD1iI1JtuxLtU1wkLBAABgeBnh6grw+a3l5EenuBoSFA9BzjAGh1OjQ6HNAUFGB2dhbT09NCnpPVaoXVapWMKrD07mQ8Kioq8J3vfAdPPPEEvF4vPB4P/uqv/gp5eXmq5lg8xIH1nkq3HIhFwsjf8fyerOeXTqdbdL/GU3480Ol0qK+vT8t7nr6X0g1CBsgqS36/X9gjxOPxwGQyCRIkKenU7OzssiEHr7/+OgDg5z//Od544w3cd999GW5R6pAlBysc5AGUauY/MDCAgYEBbN++XdglV6kNmUS6cg48Ho+wf0FFRYXkeZkmB5FIdOOy8fFx5jlSL/GioiLcfffdAKIrEB09ehRjY2PgOA6BQADbt2/HzTffzNzpWSmsLuf1k2sTEPt70saMuN9ycgQWpH4nn8+Hzs5O1NbWCptTeTweTE1NCQmjhCgUFBSkPI9ATGzFhoaUkSNHKuhz4tXVZ0ryo9abqiRFkauXZejR0qmUSqD8fmBgAOjtjf7r64t+Dg0BpGwAEYcDcDiAwsIoYZidBTQaIBKB5v77cfqGG7Dlo3lnNBphNBpRVVUlbMI2OTmJnp4e6PV6IbGZRL9Yend6DjQ2NuK73/0uAoEADh48GDNfxAYy7WGXI/bkuFjuqDbyp+Z4InIg+tp46mYRfVbkjHW9kmOEVb64/pqamrStAhQOhzO2b4Fer0dVVRWqqqqEZ67T6cSZM2cQDAZRXFwMu90Oq9WKnJwcAPFFDl5++WV84xvfQDgcxh/90R/h29/+dszxhYUFfP7zn0draytsNht++9vfokbFbtM0fvWrX+Gll17CsWPHMrr/Q6qRJQcrHMRrn6pJGQ6HceHCBYTDYezdu1eVx3S5RA5SbZyT/IKtW7cKGxgtZf1qwXEcZmZm4HK5mAazmtA7z/M4ffo0xsbGUF5eDpfLJax2dPDgQeZ1yfzuSlEBsQee7ovci12NASgeo8nJSfT392P9+vXCS4fjOJjNZpjNZtTW1iIYDMLlcmFwcBBzc3MwmUxCwmhOTo6iEZPIOChBKVdA7jcnv51YjkJfS8ugWBEMFpKROCkhUWNR7MVVilJJ6d7FEbAYEjY3B81Hhj/f2wv09IDv7QU3Oho1/gFAqwWqqoCGBuDgQaC2FlxNDfiREeD4ceCdd6JlORxRclBRAc33v49IczMip08z+5ybmwubzSZswjY3NydswrawsACLxSJEFcTPcvF9lJubixtuuAFvvvkmjhw5wjSQxeRezf0vnjv0fIpXBkWQbimTGjIvdV8rEQvy/JG6T8TEorS0VHLluFQgnbKieEA/cxsbGxEKheByuTA+Po677roLAPDxj388JmIjh3A4jK997Wv47//+bzgcDuzYsQN33XUX1q9fL5zzb//2b7Bareju7saTTz6Jb33rW/jtb3+rus1Hjx7F448/juPHjwvk5XpBlhyscOh0upQZ5nNzc2htbYXD4UANtc61EsSeyUwglbIinudx+fJlzMzMMPMLpOpfioRoFgKBAAYGBiSlX3LSHvqc3t5eGI1GnDlzBsPDw7j77rsxNjYGn8+3iBzRnla5OllIxnMMSBu9chp4KQ/q0NAQpqensWXLFmi1WskxysvLQ0VFBcrLyxGJRIS16pWiCnKGgBojJJExVAJ9r7AkT+LfNhKJLDLaxOPEml9iL+tKyAVQqpv3eoG+vigBoMnA1avXLtDpgFWrgPXrwd15JyK1teDq6oDqanAfPUv4yUlwzz4L7v/9P/BOJ2Czgb/3XuDMGfADA8C994L78z9HhNpcUk20Kj8/X1hKmOejSxRPTU2hv78fOTk5AqEtKChgjvX+/fvx5JNP4lOf+lTKvPriOaYkjRNL6qQImVTkMJ3EgUAq50Bt5EvtcaPRKBuxTgWWUlYUD3Q6HUpLS1FaWor3338fnZ2dePbZZzE6OopNmzZh+/btOHToEPbv3y+QYxqnTp1CQ0MD6urqAACf+cxncPz48RhycPz4cTzyyCMAgCNHjuChhx5SLdM+ceIE/umf/gknTpxYVqtHpQpZcrDCkSqvvdPpxKVLl7Bp06aUr4awFEiVrCgYDKK1tRVmsxm7du2KiyBlInIQDAYxMDCganMwJe+c2WzGpUuXUFNTgw8++AAejwe5ubmCwct6OZM64vXsS7U1Ua9zvOXSqy9t2rRJ+F6NB5P2cHEch4WFBSGqMD8/j8LCQthsNkEDTntLgWuGRaJ9XQ6SH5ZRJlU2TQxYkRzWd3TZ6YxGKI6Hz4fIY49dkwM5ndcO6nRAbS2waRNw771AXV30/w4HoNPFRiOiHQJ/6hTw9NPAG2+AC4cR3rED+LM/A0ZGgH/+56is6NFHgX37wAMx9xrtZWcZyOQYPSZkiUkgqu+emppCX18f/H4/CgsLhX0VSFRh9+7d+O53vwuXyxWzXHXMmCRofJN5r0YOxOoTS6okVbecI0T8fSLEghVtSzVycnJQW1ur+h2UKDIpK4oHa9aswbe+9S089dRTOHXqFE6fPo1XXnkFP/vZzxAKhXDLLbfge9/7ntCXkZGRmARuh8OBDz74IKZM+hydTgez2QyXy4Xi4mLF9nzhC19AUVERWlpaAAB/8id/gi9/+cup6m7GkSUHKxxarVbSMFQDno/u8utyubB3716mtnwlIBWRA7X5BVL1LzU5iESiS5aSpOB42iQ+Njk5CYvFgtLSUgQCAZSUlOD8+fP42te+FrMaEQHLqwzEasLJ/1l1i8tQegEmSgxYCAQCaG9vR3FxMaqrq5M2pHNzc1FeXh4TVSBGmO4jIxGIXf4QiJXuSEVzWBGaZEhFJq4F5GVPaiMoUh5ksVSMLluOhKnqk04XlfxUVwPbt18jAHV14BwO8DLGp9Anjwc4cQI4diyaf2AyQfOZzyBy331RgvHd7wJtbcDHPgb8n/8DWK3M6A0tNYnXQOZ5PiaqQEe/BgcHodFc24Rtz549ePPNN3HvvffK90umbhZ4/tpmholcrwQ15FVN3XLPLlqiRuYWTdRSJYXiOA51dXVLIlVZLrKieKDVarFr1y7s2rULDz/8MNxuN95///2YfkhFa2moOUcKLpcrzlavLGTJwQpHMpEDepff3bt3L8vQolokGzkYHR1FV1eXqvyCdNQfL3ieR29vL+bm5pgvnXg8wIODg3C73WhpacGOHTvQ2dkJi8WCkydPorm5WbJcseElp+tWkhHISZ9oQ491fjwvZJ/Ph8uXL6Ourg7FxcUpl6IQI4vscuv3+9Hd3Y3x8XGMj4/DbDbDZrOhsLAQOp1OMVIhHjOx5IK+Z8URHbHHNZH+qMFSyYXkCIYSOSbRC6l2iYmq0C69HnjrLUA0foreb54HLl6MRgn+67+iqxM1NQGPPALu4EFEcnKA558H/u//jZb9yCPA7bcDKuRXcpAzkGnDFgAKCwtRWFiI2tpaLCwsYHp6GiMjI6ipqcFzzz2HlpYW2Gw2wUAl84g1buK6pYclcWKQrANGru54iAXP84uIPk0UxM8u8biw5o64bxUVFYoLgaQKKyVyAEg/yywWCw4fPhzzncPhwNDQkPD/4eHhRU4/co7D4RCS+1eiciIdyJKDFY5EycHMzAzOnj2bkJd8OSLRyAHP8+jo6IDX60VLS0vCnpqljhwMDw/D4/HEyA3oF5XUWNAvplAohK6uLuTm5mLjxo3QaDTIzc3F1q1b0dzcjKNHj2JoaEgIu4r7SL/00pVYy9LsszT8LK8yaR8ZH6fTiYGBAaxbtw4FBQVp0/vT1+n1ekG2UVJSInhre3t7kZubK8g+8vPzEzKU4/EmkzkhNmBookG3nYydkvc9GZlSurzIcmNFjrPuEXpshE8JpwndfsHjPD8PzcsvI/L000BnZ5Rc3HEH8IlPAGvWRK9xuYAf/jBKOrZuBb73PaC8XFWf0yWhIjk1ZWVlqKqqwhNPPAGn04mRkREAEPZVMBqNikRTPL8ISOSAbks6vO5SbVKSMslBfK3YkSFH6AnE85FATCzMZrPs0uGpxnLNOWBhfn4eBioPRw47duzAlStX0NfXh8rKSjz55JN44oknYs6566678B//8R/Ys2cPnn76adxyyy1pl3GtFGTJwQpHIgnJQ0ND6O3txbZt22AymVLWFrWJPOlAIp57ssGb1WrFzp07k2r7UpKD8fFxOD/SPovlPRwXu4LIIkPno5ek3+/HpUuXBDmM2Kuo0+nwox/9SIiiSGnvyWc6DO14ymVFKsg4RCIRIfG4ubkZubm5MefRn1J1yOUgqO2rTqeDxWKJiSpMTU2ht7cXfr8fZrNZ0IDHu0OtkldUbvUnufGXk1qw5D30ZzqjEenKqyCQknFJ/b5cby/w9NPQPP88eL8fXH098O1vg7vtNvBUkjr39tvgH3kEEZ8P3De+Af6BBwCK3KfTQFbrOS8oKMDOnTvR19eHO++8E8FgEG63GyMjI/B6vSgoKBASm4kMVUzGWORdPAfpOSWOerHaJjX2mSAW8Uhx1I47EF0xatWqVarKTRVWUuQgnmVMdTodfvrTn+LQoUMIh8P4wz/8Q2zYsAEPP/wwtm/fjrvuugtf/vKX8Qd/8AdoaGhAUVERnnzyyTT3YOUgSw5WOOKJHEQiEVy4cAHBYBAtLS0JbV2u1I5UlhkP4jVESH7BmjVrUP6R124p608Ubrcbw8PDMd/JvTzF0pJIJAK3243u7m40NjbCbDYvIgYcx2Fubg52u13wKoklLOL/SyGVuQKJlEsnHpPoCI14ZD00UVDKFWBdK26vXq9HRUUFKioqwPPXVpbp6+tDXl6e4K1NZ5RDDrR3PV4Nt3hOssZdSqKSCuM+0WvjMrADAeD116PSobY2aHQ6RA4ciEYJNm0COO5aIrLPB82jjyL87LNAYyPwz/8MvqFhUdlSZFVObqem3Uq/lfjY/v378fLLL+POO+9EXl6esHEVz/OYnZ3F1NQUOjo6EA6HYbPZYLFYUFhYyHwm0Em8UiScJvLitqnNRxGXzZLVsUhLIvOBlJnKiAXHRfMMltpQX0k5B/Hujnzbbbfhtttui/nu+9//vvC3Xq/H0aNHU9a+6wlZcrDCoZYczM/Po7W1FeXl5airq0u5hz8TCbni+tWSpJGREVy5ciWlkZOl6P/s7Cz6+vqYdSu9gEj7RkdHMT4+jqamJmH5NXHbOzo6cPz4ceGFvnHjRtx2223MFwg5B5D2wotJBTkn3dGGhYUFdHR0wG63o7KyUvFatR5llkGrtk1ykYri4mIUFxeD53lhvfqenh74/X5YLBYUFRXBbDbH/A7p8qCnSi4kJelheZfFZdCfBOK5RspWI09JlnQI/RoeBn73O+C55wC3G3A4wH3964jcdRfwUVQoBm1t0Dz8MCKjo8AXvwj88R8DouWRxREqMQkj/WSBjpqySBhLLqb0/L/xxhuxevVqpl6ebMJWXV2NcDiM6elpOJ1OdHd3Q6/XC1I5vV6/KKIgbl8qnpusMSNtVWOYi59P4vnLKoc4wlIZsaiurs7Izr/Xa+Qgi+SQJQcrHFqtVnF9/YmJCVy8eBHNzc3M9YBT1Y5MboSmhuzwPI/29nb4fL6k8gtYSDc5CAQC6OnpYdYh5RWj2xYKhYSVjZqbm4WXgbjd8/PzeO6552A2mwX5TVtbGxobG7F27dqYcsVSLvqFGo+RpuQtpctWMvAI6MRjkmCWKgmTGGqMSnE/lEiFwWBAZWUlHA4HwuGwsMldX19fjAFmMBiYCcj0ZyJtlsNSeu6lIjc0aGLA8r6L83JY46PYrkgEkbffjq449N57USnQjTcCR44AO3dGNzgTj3cwCDz2GDT//u+IlJcDv/gFsHlz3GMibqu4716vF0899RTeffddGAwG3H777Thw4IDg2RY/l+n5yIoKAlFpUUNDQ8x9wRp3rVYbQ2rn5+cxNTWFrq4uBINBQSpnNpsXkZJM5xGQPknlE8iNOfmUIxZybRT3zWazqVo+Mx0Ih8Np23051ZidnUVBQUGmm/E/AllysMKh1Wrh9/uZx3ieR3d3N5xOJ/bs2ZPWjToyTQ6UQPILioqKks4vYCHRhGg1CIfD6OnpWZQ4Rl46cnknGo0Gfr8f7e3tsNlscDgcsrkCTqcT4XAYeXl5OH78OG688UYYDAb09PTEkAM5769aA17cj2RJBXk5u1wu9Pf3Y8OGDcjPz1dVbqKGtBpvNN1HteXS7dJooisgkXXn5+bm4Ha70dnZiUAgICxBSfZVkCpD3A45WU+iRCjduQDxXCuOWqj5/ekx4Tguuq/BM89E/zmd4IqLwT/4IHDPPUBpqXS7u7uBhx8G19WFyN13A3/+5wDDqElFAvIvf/lLtLa2Cm1/4oknkJ+fj3379qkuW+o+Zj1XyHyi81HId+KogtvtFhLwCZkgBl468wTSSSx4npeUQdEEQWpMyT/yDDUYDKiurk6oLanA9SwryiJxZMnBCoeUUR4MBnH27Fnk5+djz549aV+NYDmTA7Iy09q1a9O2CoQaaU8i4HkePT09mJubk62XJUMIBALo7++H0+nE+vXrYbPZFNtoMpkEqZDNZkNnZydWrVoV49USGwU0kjG04zHgxX+Ta8myrBs3bkROTg6TGIgTISOR2N1OaaNSKeFfbV9TpXUGol7d/Px8VFRUCMvvTU5OoqenB3q9HsXFxbBYLNDr9YsMZDn5CnBt3xTa0y72kIrnuhpplRKS1cwna2DT48GHw8CHH4I/dgzcG29Ej+3aBXzzm+D37YvuTfARSPRMmFM8Dzz+OPh//EdwRiO4Rx9F5MYbY+pIVbs1Gg08Hg/a2tpgt9vx/vvvY/369TAajXj11Vexb98+yWuTlY3RxEFKCsVxXAypvXr1KpxOJ/r7+zE/Py9EFaxW66JcNTnvfbqJg5q5KH5mqIX4ftRqtaitrU37+1kOWVlRFixkycEKB8soJ8m2jY2NgtY6E+1YDhgeHkZPTw+2b9+e1nWj0xU5GBgYgNfrlayTZaTzPI/z58/j6NGj8Hq9sFgs4HkeN9xwg3AOK/wNRHXvW7ZsQWtrK0pLS/H222+jubkZGzdujDGm6frVIhmvsvhccbnBYBBdXV3Q6XQxicescsWRCikvHz2n5XIF6HJJOeJr4yGO8YyrTqeDzWYTiJ/f74fL5UJnZydCoRAsFouwr4KSAULmsDiawPM8c56x2iwnEWPJN8ixpYwoSB53u69tVjY0BK6wMLqa0Cc+AVA7rdLXxtzzY2PgH3kEaG0FbroJ3N/8DcIWy2K5EQVyT4lBzyXWcVa/6uvrhb0zlOacUr5HOozrnJwcmEwm1NXVIRwOC5sF9vf3Q6vVCkRBKg+MHiuWnIf8nYycLp7jan8XueOrVq1Ka0RfDVbSUqZZWdHSIUsOVjjERvnw8DC6u7sT3swrUWQ6IVmMSCSCjo4OzM7OYu/evWnfaTId/R8bG5PchVHOSHe73Xj88cdhMBiwbt068DyP1157DTU1NXA4HLISDI7jcPjwYTQ0NKC3txfz8/O45557BG+NnAde/L243FTJemjZh0ajwfz8/KLEYzWIh6yozRUg14r3FGDpk1m5Asl40LVaLQwGAxwOh7Cpj9vthtPpxJUrV5Cfny8YYGKDJFVyISk9vxxxlpo7Uueo0XSL28WCRqNBJByO3awsGASam4E/+iPg4EFA4rkRUzbPAy+8EN3QLBIBHn4YmrvvRkTBAJeK3shFyUi7yVwpLCzEli1bcPr0aRQXFyMYDGJ6ehr333+/5NhkijjQZFyj0cQs60s2YRseHsbs7CyMRqMwV+lN2KTap9RmUqf4PhRfv5QRiZKSEiGqkklkZUVZsJAlByscRPYQiURw6dIlzM/PpzzZVg2WU+RgYWEBra2tsNls2LFjR8rzC1hINTmYmprC6Ogo85hc0lswGMTvf/97RCIRVFRU4MSJEzh8+DA0Gg0GBwdRXV2taORpNBqsXr0aq1evXrTrJKsdxFBXKxdiJUSKfyM5UkG+02q18Hg8uHz5Murr6xe9aJPRzsshEflTJBIRxlaN1IjlgadJET3uUuOv0+mEZFGO4+Dz+TA1NSVEFehchUx57qVIGN1fubJJ38V5J/ScYnp45+YQeemlKCm4cgUwGIC7745GCRob1ffZ7Y5uaPbGG9Fk4+99D5qqqrSNJ4uIfelLX0JBQYGQkPzAAw+gpaWFOb9I3VIGspxenq5TqW3xgt6Ejed5eDweYcdmILoJW3FxMQqoPSNY9csRBxIBUwOavJOyaWJBjyVpTzzzvKCgAA6HQ1Vb0o2srCgLFrLkYIVDq9UiEAjgvffeQ0lJCZqampbEGGa1I9PkgOM4TE9P49y5c1i3bh1KP0oYXAqkkhz4fD4MDg7KerhokBfP/Pw8Ll++jPLycphMJmg00R2Pe3p6YDabUVhYmLD3Xiq/QGzwSrVNqg8kv4EFKVKh1WrBcRwmJycxMDCApqYm4YVBe/bldolO1DufTkOZBitSIZUcCkDWICbHTCaTkCxKPMxkCUqDwQCbzRazsZWaNqczFyCeaJKYkLGMaABAdze4o0fBv/ACOL8fXGMj8Fd/Bdx6K/iPdqkGri33Ket5//3vge9/H/B4gD/5E+BznwOX4uUt1SA/Px9f/OIX8aUvfUnxHhbnCaipm/a8k2ulpFBKdUvJV8RyHbPZDLPZjJqaGgSDQczMzGB4eFjVJmxK5Uu1T4mYiucbPb9YMjrxJy05TMdy4oliJcmK5ubm0rbiYhaxyJKDFQ6PxwOXy4WdO3fCbrdnrB3LgRyEQiGcO3cu7fkFLKTqQe/3+4WViaTqYSWRBgIBdHR0YM2aNSgoKMClS5fQ19cHh8OB8+fP45577kFjY2NCbZIzGgB5j1ki5ZKypUhFOBzG0NAQPB4PmpubF603LjakpQxmcblKsp5kjN10EhI5WY8UqdDpdCgpKUFZWRnC4bCwsdXly5fB8/yiXAXaM6+2v8lov1NJOjShEPDii9EowfnzgE4H/tAh4MgR8E1NAJkLorFjkWGO48DPzkLzD/8QzU2orwf+6Z+A1auF+ZMoKZUaE1pCl4qIQzx1k/rlyBi5njVe4r81Gk2MIUrntEghNzc3ZrnU2dlZuFwuYRM2QhSUNmFLpO+JHhc/U+g5UV9fv6yWDl1JsqLZ2dmMruz0PwlZcrBCwfM8ent7MTo6CpPJlFFiAGQ254BIqgKBAG688cYVm7BE9iIIhULM41IvodHRUSwsLGD79u2CJ+3Tn/40Lly4gO7ubpw5cwYHDhyI8QgDbO+WuGwluVC80Qa5vqi5LhwOw+/3Y2FhAU1NTYuMAaUXtdo2SY1JIqSCJExLIZOEhBgtBQUFKCgoQFVVFUKhkCDp6OzshN/vx9jYGIqKigSjRm7jLRbEXtkliSgMDQHHjqH5mWeA2VmgqgqaP/szRG6/nblZmZroWSQSAd58E/yxY8Af/AHw1a9GNzT7KILGIga0511OriN3LB0Rh0X9SrBsOVJDHyfnsGSC4vlBfy++FwsLC2EymbBq1SphrkptwpauviV6vLy8fElzAdUgKyvKgoUsOViBCIVCaGtrQ25uLvbs2YN33nkn003KWORgYWEBp0+fht1uh9VqXTHhUTF4Prpk6cLCAvM46yUUDodx5coVaDQa6PX6GOM/Ly8P27dvx/bt2zE8PIzXX38dq1evXlSnklHLepGTT+LNFI+5kgc1UUOG7His0+lQU1OzqN5kDAEpz6hYtqN0rRypEBuHaow+OSSj8Zarl0QV7HY7eJ7Hhx9+iIWFBbS3t4PneSFXwWQyMdugRFjIpzhPgPxNn8fyRstGFIJB4O23o1GCDz4ANBp4N22C9cEHodm5E4m6L2L6efgw0NAAUJE4Jc87TcTiqRO4JqNj5ecoEXiltqlpQ6qMY1qfL3e9mMxL5egA0RWQ7Ha74BwjO4t3d3cjEAjAbDbDZrMJO4vTcjE15FmO9MR7fWFhISoqKiTPzxRWmqwoSw6WBllysMLg9Xpx5swZ1NXVoeqj5fXkvF1LBSJtWUq43W6cPXsW69evR2lpKT788MOMRS+SRV9fH3w+H/MY6wVKDGW73Y7y8nKcOXOGeS3HcbjjjjvwzW9+E3/8x38c8xJIxOsszhegPYJ0uVK7stLyAla5UvV6vV50dnaivr4eIyMjsomHLCyVd55FKgBIjpMSqSDfseRC6YooiNul0WiwatUqwVNLkuV9Pp+g/y4qKkJOTo4qQ5Ql26E963IkTJwoKlw/Pg787nfgnnkG/OQkYLcD/+t/AXffjZ6BAezcuTN1BjTHqSYGao5LER5iwJJIIstIViLw9Hk0sYh8FOmQG28lxHvf8Dwf46FOh9c+Pz8f+fn5cDgciEQimJ6exuTkJLq7u5GXlycQ2/yP8kvEkQnW/0nbgWs5UmpkpPS45ubmora2VvGaTGAlRQ6yS5kuHbLkYAVhdHQUXV1d2LJlC8xmc6abE4OljhwMDQ2ht7cXO3fuFB4Wct7q5YyRkRG43W7JBGSxHMbj8aCrqwsNDQ2wWq2KHu01a9YgPz8fZ8+exbZt22KOsZCMXlxJYhBPueQFPDExgcHBQSHxeGxsLMaTmkgERC3kDCC148Q6T4lUqPl9WEYg/T0dqVATAVGqF4h6aktKSlBSUgKe5+Hz+eByuXDp0iUAEHIVjEajKi8x3ad48yoQiQCnTgFHj4J7++3o93v2AN/5DtDSImxWphkakiQVautOVf5DvMcB6XsmEc+2uCwpOY+4HvH5SoRCqe6lkPsAEPYAAYD5+XlMTU2ht7cXCwsLKCwshNVqhcViEfaHIO2Uk4hFIhFh0zY5Uk/K4jgOtbW1izZ6W05BS2trAAAgAElEQVRQQ3aWA7KRg6XD8p2tWQiIRKJr9vt8vowsU6oGS0UOSH7BwsICWlpaYh64tA56pWBychJXr14FoE5CcfXqVYyMjKCpqQkGg0FS3kO/fEn04Pnnn8e2bdvSJkdJxshilRuJRDAwMLAo8ZgkMNKadxapEHtOCRLJQYgX6b5W7HVXey0rSZT+P0viI1U2x3EwmUyCvCgQCGBqaoq5Vn1eXl7qxsPtBp57Dvjd74DhYWjMZkQ+/3ng3nsBxvKQhECyfmc5I5AcV/IUp5s4qPVUJ1u32hwa8fWs+018X5HxJxIpVbkdKewbABgMBlRWVgp5NTMzM5iamsLAwAC0Wq2wWpfRaFQ1V9Xeg5WVlUu+QMb1iiw5WDpkycEyh9/vR2trK+x2O3bu3LlsGf5SJCST/AKpJVtXWuTA4/FgcHBQ1bk8zwubkm3atAm5ubmC4QBgkbEsHodbb70Vjz766CICIa4j0VyBVEcbwuEwOjs7kZubK+zOzKpLzsgR/y1Xr5QHUIpUxNsfsdc0UUKSSnlUvJ5cYqRKPYNyc3NRVlaG0tJS8DwPr9cbs1+H1WqFzWZbtFa9qj7xPHDuXHSFoFdfjW5WtnkzNF/9KiI33xxNCpa4PhHjXelekGo3TaykEpDjzRNgkYPlkkdA2kd/So2bGvkTfUzqPk4FsdBoNLBarcLeKH6/H9PT0xgcHMTs7CxMJpNAFmgHlEajgd/vl4xCicfGarUu6ZLa1zuy5GDpkCUHyxhTU1M4d+4cNmzYgJKSEtlzE/EupRLpjhxMT0+jra1NdiwyHTkQe17lMD8/j97eXlnDhRwLhULo6OiAyWTChg0bZPsp9WIvLi7GD3/4wxgPKsszLJUrIKX3JlELVnlKbSLXs/Ip2tvbUVpaisrKSsmISiq982qjCeI2K5EK0k5iVCvJlJIhBsnIheQgRyqkyuY4DoWFhTCbzUJUweVyCVEFk8mEoqIiWCwW5OTkSLff54suQ3rsGNDdDRQURCME990HrrFR9S7E8SLR30LJQBafR9dHf5IyxH+T+y1e0kLw0ksvQafT4cCBA8zj6fLaA9dyDsTPn3giX7RUT+o5y8oVUIJer0d5eTnKy8sRiUTg9XqFHZs5jouRy0k948Vjk5eXh1WrVqmqPwt1yOYcLB2y5GAZgud59PX1YWRkBLt27VJkyuSBmcmkonSSg8HBQfT398fkF7CwFNELOaj9HYLBILq7u1V56GdnZ9HR0YFVq1bBbrcvqawHUF5pRUqyoUQqpF7eJPG4oaEBRUVFzDYpGdnknKWQC6nR9NN5I8SwIeeK2yvlMU2nTCmV0QgWiEa7tLRUiCqQHXDJZn8kqZlEFbiuLmiOHQP/4ovg5ueBtWuBv/kb4NAhID9f0ehLVrOeDNFKJAFZzjMulnLJ7eFBzxf6/+QzLy8PTz/9tCQ5kEOyciAlxDOurGeOmuvlck9IuVqtNmYTtkAggOnpaYyOjsLj8UCv1yMYDCIQCEjuV6DRaFBfX79iEn1XCubn56HX6zPdjP8RyJKDZQaykZdWq8XevXtVPVyIYX69kYNIJIKLFy8iEAhg7969igldmZYVqSEHkUgEPT09CAaDki8pYiS6XC709vZi7dq1MBqNaTMQky1XTjoh93uIvW8TExMYGhqK2fFYStaTCWM3GUICLF5tRq3UiJwrRSrEZaUy8VMOiRjB5HuLxSIYXwsLC5iensZQdzfyfv97lP/+9yjo7kYoNxfcwYPAkSPAhg3RVYIAICKd5E1/krlD5+OokfQkKkUidaVrvFl1i6VuUrkVpO69e/fikUcegdvthtVqVZT0JBp5YZUZDodlvf3pHFcxsYjn+ry8PCGqwPM8xsfHMTw8jI6ODkQiEUEuRyfhV1dXw2AwSLZnuSBVv+9SQYncZZE6ZMnBMoLP58OZM2eEZQPVQqfTZVxrn2qvPcm1KC0tXaQ5l0KmZUWEnMgljPf19WF2dhaAtDyD53kMDQ1henoamzZtEmQX5BwCKYOR1S61Bi/R3paXlwvHE5ULqfW+8jyPgYEBeL1eNDc3C/kUUqClCWJDmZYcEdCGTqIe4WRkO6m4Vm3yo1QZrPlBRzTE5Sq1O5WkI298HGXHjqHs+ecBjwd8VRWcX/gCRrZsAW80wmY2w/qRnIDIauQkPeK/xfk4LAmUeM7Q46XWUE6XgUtHm5KtW6/XY+/evXjzzTdxzz33qI5M0XsExJsjID6PhVTkEUghFZEe+rher0dBQQHWrFkjJDaPjo7C6/XCYDCgvr5+xejiM604yGL5IksOlgkmJydx8eJFbN68GRbG7p1yyNQGZOlqA8m1aGpqimvn5+UQOZB7yQ0NDcHtdkteG4lEEAqF0NXVhZycHGzcuDHGYJEyiFgeQ1rrTsoXX0c+6Rf7m2++iRMnTuCnP/2p6mhDvPku9LV04jHZ8VjpRQ6w13xXE6kQkwp6fEiiIl2uGs+aWjlDItcmU6+cB1iJsBBjkHjdWWRLqgxV7QoGgbfeim5W9uGHgFYL3HwzuCNHgG3bUMxxKEY0/4SsKDM/Pw+LxSL8Y0USEyE0YiIhBXG/6DlE34fictVEK5S0+krPFjmI6/74xz+O48eP45577mEeZ7WNvq9YTg01EUIi2RHPJSWvfjJIlliwjtPPiZycHGG5VBLRtFgsOHv2LAKBAOx2O0pKSlBUVLQsjfBMKw6yWL7IkoNlgoKCAuzdu1dSwyiH64kcDAwMYGBgQFWuBasNyyFywILT6YTT6WQeIy8gv9+P9vZ2IYRNH1dj8LAiCUovPnIdwdq1a/H9738ff/3Xf43Vq1fj8OHDKCsri7kuHA4vMhBZ+nkWaEPA7/ejo6MDZWVlQn/VeNjVJAPK1UvXQ9pONppSUy89buLcCnEf0uV9T/ZapXEm85gYPGKjWEouJEVGSVkapxPhY8eAZ54BXC6grAz46leBu+8Giouj0iGqbFrSAUQ3PnS5XBgYGIBOpxNWlMnPz0/q/k9kPMWSHjUJyHKRPiliqkS84yWYLS0t+MEPfoCZmRmYzeakvPbxEFQyPvT5cuNGokRKzoelfuZLSVt0Oh3WrVuHvLw8rF69GqFQCC6XC2NjY7h06RL0ej1KSkpQWlq6bJJqV9LuyFksLbLkYJkgGX3iciAHycqKIpEILly4gFAopCq/QKoNwWAw4TYkC6kxmJmZwfDwsOR1PM/D7Xaju7sbjY2NMRvcqfXei430RKQsPp8PTz75JMrLyzE5OQmj0Yh///d/x0MPPSQQNVq6Q8oh39PlsiIVtKFBJx6TSJlaUqHUNzV9JYhX/kR/qjGcxARCrv545UJq2pzqa5WOM49FIsD770Pz9NMInzwZNf5bWoAjR8C1tESjBh+BJVshBEWj0QhRA+CaBK6vrw9+vx9mszlmU6t42p2o7EvNcdZvrHb+0ve11NiQ81jlstqWn5+PnTt34q233sLdd9+dsoiEVNvF38m1TXxuokvJ0vVLRU0TJT50RI0+XlNTg7y8POH/dBI+EF1cYnx8HBcuXMD8/DxsNhtKSkpQXFycsQ3SVlLkQI28LovUIUsOrgNotVpZz+dSIJmb1u/34/Tp0ygvL0ddXV3CZS2HyIG4/rm5OfT19QnHgcUv9NHRUYyNjWHjxo0xL5d4koiljHK17QQg7KPQ3NyMkydPYsuWLRgbG0Nvby+ampqYZZEXLJEw0R5n1nlANIpCEo/JRm6sqIfcS1ytd365GNnEwCVQajNtENKgI0JSxlcmohFMTE8Dx48Dv/sduNFRRCwW4AtfAO67D6ioAADwAEBJS5TGhG6rwWBAfn4+KisrEYlEhE2tBgcHkZOTIySKxmO8s46lW88uVzc9b8TSwbm5OWi12phnBg25PIGDBw/i+eefx913352wPEwJ4jLF0bd05BGwcijU9E387GERC1IO0enT15eWlirKgQsKClBXV4e6ujqEw2FMTU3B6XSis7MzZudxsqngUmAl5RzMz8+vmFyO6wFZcnAdYDlEDhJFovkFLKQ6KTrZ+gOBQMySpeKXFM/zuHLlCkKhEJqbm2Me0rTmmwVxrkAish6pMsvKylBfXx/zcu3u7sbbb78Nv9+PHTt2YNu2bTFkR83Y8/y1xONNmzZBp9PF9ENKliN+iRMiwkogTZXOOxmjjmV4qI0KiNusxhNMHyNlSCFRL7FqI5jngba2aC7Ba68BoRC4LVvAP/QQcPPNACNZPxEDmzVXyPKTtbW18Pv9mJqaQm9vL3w+H65cuSJIkFjGkNT8kYPU/PL7/QiHwzCZTCkhW+K2uFwu/OxnP0NHRwe0Wi0OHz6M+++/P6ZfYq87z0c3UXz//fdhMBiwY8cO/O3f/i08Hg9MJtOifslFu+T6Th9nPe/USliSkTolcjye54b4+WQ0GlFZWSl5PgtarRZ2u114583PzwtEwefzwWq1oqSkBHa7XXaBi2SxkiIH2Q3QlhZZcnAdYKWSg/7+fgwODiaUX8DCckhIJi+VcDiM7u5uSZlTOBzGxYsXYbVa0dDQsCjcLkUoAPlwvZyBqGQY1tfXIzc3Fx6PB1u3bsXMzAz0ej1CoRAee+wx6PV66HQ6/OY3v4HL5cLhw4cXJQizwHEcgsEgurq6hMRjsQxJLeT0y+I6pYgTDVauwHLOBVAyWuIlhazxSKhdHg/wwgvRzcp6ewGjMboE6X33AfX1MXkE4rLT4XnX6/WorKxERUUFTp8+DZvNJpCFvLw8WK1W2O12Sa87qZtefpNFwOn6g8EgfvGLX+Dpp59GRUUFmpqa8JWvfCVGJphIv2lywPM8fvKTn6C3txdFRUUIh8M4ceIE7HY7Dh06JFwvHpPXXnsNP//5z4X+PPXUU1i/fj3eeust3HHHHXG3jfWcpe9pKXIlliWyEK9scKlBO220Wi1qa2uT9vQbDAZhlcJIJILp6Wk4nU50d3dDo9EIUQWyqWCqsJJyDrLkYGmRJQfXAVYaOQiHw7hw4QIikQhaWlpS5rlYLrIi4qWbn59nnjc3N4f29nbU1tbCZrPFHEvEI0fXrWR4skgF+VdYWIgvfvGLeOGFFzA6OgqHw4Fbb70Vzz77LPLz86HT6bCwsICysjK89dZbuOWWW1QZEnNzc4sSj5Ptq9K1NOgy1EY5WBInuj1SCchyyFQugNxYicdDqi+SZLSzE/xTT0Hz8suA3w+sWwc8/DD4Q4cAvT4uL2w8fVJznAbZZA2Iemndbje6urqwsLAAi8WCoqIimM1m4VnEIuhK0Z8XX3wRJ0+eFJa0vHDhAv7lX/4Ff/mXfykb2VOKDtGG9tTUFPr6+lBUVITx8XEYjUYYDAa88cYbAjkQlx8KhfDLX/5SIPdANL8IAF599dUYcpCMV14pMZtIWMSed/GnmFjQ45/snEiFDIyWR9XV1aXcs6/RaIQVkNatW4eFhQU4nU709PQISeSlpaWK5FYNVpKsKLs78tIiSw6uA+h0uoznHBAohePn5+fR2tqKioqKlHhcaGQ6ckDIyeDgIDweD/OcyclJ9Pf3Y926dcwHXaLGkhIxkjP6aAlCRUUFHnzwQeF7jUYDn8+HnJwcTE9P4+LFizh48CBCoRBCoRBTfkB74IkRRicek2OJ9jVdhjKrXazchnhzBcRyD3G5ybY53aRjUX/9fvD/9V/gnn4a4fZ2IC8POHwY+MQngPXrr13LkISJP1ljnW4j0GAwwGAwoLy8HOFwWMhV6O3thV6vF4iE1E6sUmW/9dZbMJlMKC8vx8TEBKqrq3HhwgX4fD7VRg0Zb/p+IsmvGo1GWM0uEokgGAxicnISNptNaCurbR6PBwsLCygsLMTQ0BAMBgMKCwsRCATQ3t4On88Ho9Goqn3JyH1Y9474N1ebgCwXzRHPWVYeglL5cseJQV1RUbFIkpUO5OXloaqqClVVVeD56OIVTqcT/f39iEQisNvtQs5DvFGArKwoCylkycF1AK1Wi4WFhUw3g+n1oeFyuXD+/Hls3LgRxcXFKa8/05EDjuMwPj4uhO7F3q+BgQF4PB5s2bJF0NuLr08kV4DUk4hcRU5uQl72W7duxYsvvojy8nK89957GBwcxLp164QdQVkRC41Gg6tXr2JoaAgbNmyIWe2IfNIeOCD2JS63vGEi8hmlcVBzbTyGhdg4oRNLadDGjNr8ErVtJu2W6nPcpKO/P5pLcOIE4PMBNTXA//7fwO23AyIjSSlPQMkQFEvCWM8WcYK/WiOQHhOtVrsoquByudDV1YVAIACLxQKbzQaz2SwY6FJl6/V6+Hw+lJWVIRgMCv0Uk0O5OciK4JClg3meh8lkwu7du/Huu+/CZDJheHgYRqMRd911l+CVFz97ioqKYLFY4PV6UVhYiMnJSeh0OuzYsQNmsxknT57ErbfemtRcUgO5OR5vxCJeKaB4/ki9o9SQd57nUVhYGBMFXSpwHAer1Qqr1Yo1a9YgEAhgcnISAwMDaGtrg8lkEiRIalZAzMqKspBClhxcB1gusiLSDvHDhud59Pf3Y3h4GLt3707btvKZTkj2+XwYHx8Xlq4jL5hQKITOzk7o9Xps2LCB+ZKVMxDljGH6pcfqu0ajgdfrxcWLFzEzM4P6+nphRSi143XTTTdhcnISZ8+eRUlJCbxeL+6//37BuGeV0dvbuyjxmPRFLqeCPiY2DEl7tVqt0P54vM1ySPe1Ur8fTWjV5peQ7+n6WfXFI70SQ+hTMAhrayvwi18Ap08DOh1wyy3QfPKTiGzeDEjoylPl9WdJetQSPGIkE6OefCdXVn5+PgwGAxwOh7D77eTkJHp6emAwGGC1WiWjCnfeeSd++tOfoqCgALm5uXC5XDhw4ICsV5+G1G8tJkVf+cpXUFpaipMnT8LhcODee+/Ftm3bZDcq+8Y3voEf/vCH4DgOs7OzqK2txQMPPIAPPvhAkBaJnz/02CebD5PMXFQDJdIiFbEA1DkN6M+cnBzU1NQk2NLUIjc3FxUVFaioqADP8/B6vXA6nThz5gxCoRCKi4tRUlIirNolxkqKHGRlRUuLLDm4DrAcljIl7QiHwzEazHA4jPPnzwMA9u7dm9YHUSZJ0uzsLEZHRxc9gOfn59He3o6qqiqUlJQwr5XTfDNlHdQxIPpyow1mGjMzM3jsscfgdruh1Wrx5ptv4uabb8bBgwdVGyo5OTn4zGc+gzvuuAMdHR145JFHhHC6uH1kh2dx4jGrr6w65byDhCTxPI9wOLxIskLICotksRJIE/E0K7VZDDmvXDJGNMtoVrpWSoohLpPjOPCjo8Dvfgc8+yzqp6aA8nLgoYeAO++Exm5P2NBLp0SKNX9IVIskkcpFpMRzJzc3V1hRJhKJblI4OTmJzs5OhEIhIapQWFgIrVaLXbt2AQBOnDgBv9+PW2+9Fbfddpuqfin91vR9lpeXh09/+tP49Kc/rXpcNm7ciMceewznz5/Hb37zG9xwww0oLi7GjTfeiB//+MfweDyShlc8ch7SXvqTluOw7odU5AEoyZ2SjXjQ90Z5eXlCm5WmGyRvrLCwEA0NDQiFQpicnMTY2BguXryI/Px8IapAfuuVlHOQjRwsLbLk4DrAcoscEMzPz+P06dNwOByoqalJaX4BC5mKHCwsLKC7uxtArLRnenoa3d3dWLt2raQ2NRkpiziiQBvMpNzTp0/D7XbDYrHA4/GgrKwMb775Jnbt2iW5Ljedg0DDaDRi586dMBqNOHv2LLZt2ya0A2DveKy2r0oQGyhSnj/ySdejRqYkJTdQk4Og1OZEjJN0EBZFCUY4DLz/PvijR4F33gF4Hty+fejavBlrPv954CMCShur4rFPl6xLzXEp0BI5uXPkIjgajQZ6vR4OhyMmqjAxMYHu7m4YDAYUFxdj69at2Lt3b8y1YiIbb7+Unptqx8VsNmPfvn0Ih8P4zW9+g89+9rMwmUzYvHkzTp48icOHDzPrliPsavMEyG9AnBji8hLJxcnEcYfDgYmJiRUhxdHpdCgrKxN2uPf5fHA6nbhw4QL8fj9sNhtCoZAgqVvuyJKDpUWWHFwH0Ol0y44ckPyC5ubmRSvypAuZSEgOhULo7u5GKBSCRqNBKBQCz/MYGRnB5OQkNm/eLLmaRSqlLPT/6b+vXr0qaKHPnz+PAwcOQKvVwuPxoLCwkFmueAw5jsPFixdx7NgxfP7zn8fhw4fxwgsvYMeOHYLXyePx4MqVK6ivr2eSjmSM3aWU/NB/K80nJf2yVB3kmpTlAqgsV/Jalwt47jng2DFwV6+Ct9mAP/xD4N57wZeVYeb0aUQ4Dhwjb0JMlmgyJNa+k3Po69RqxpOV5KSalOh0OmFFGY7j4PP5MDU1hY6ODoRCIUF+RKIKrN+f/mTJechxcW4Ofd758+fx1ltvIT8/H/v3718kd2G1fc+ePXjkkUfgcrlQXFyM/fv347XXXmOSAznES7gikcgiL7ycZFJNLo7c75tqYlBUVISSkhKMj4+vCHIghtFohNFoFDZhc7lcuHz5MiYnJzEyMoLS0lKUlJQIuWTLDVlysLTIkoPrAMslckCMqd7eXoyMjKQ1v4CFpU5I5vnokqULCwsxGv4rV64AADZt2hRjGLBe+lKI11iWyj1oaGjAhQsXUFFRgf3798Pv90Or1TITwqVelqFQCG1tbThx4gS8Xi80Gg3effddfPOb3wQQJYJTU1NYv3698HuzDGcpPXO80RN6bOSuTSchkZOCsSIb9N9SpEJNdCFlRInngTNnognGb7wBhELQ7NiByJ/+KfCxj0VzC0RQa2CLZWBq2i0ldaK/S9S7LGfopCo/oqCgAAUFBaiqqkIoFILb7cb4+Dh6enqg1+uFDdjI0pNqcihI28TedfJ5/Phx/OpXv4LX64XFYsHrr7+Ohx9+GGvXrpVte15eHlpaWvDGG2/gyJEjcDgcOHnyJB566CFs3boV9913n7DyTabyBJQiOUrkmkW66HrlSIm4fiCabL5q1SoAsfscrFRotVqUlJTA5XKhqKgIJpMJTqcTHR0dmJ2dFYhQcXFxWjdhiwezs7NCPl8W6UeWHFwHWC7kgOM4XL58GXq9Pu35BVL1LyU56O/vh9frFf4fDoeF/QHIsnOs9tAveSnDRcojJvXClnpZbt68GR0dHejq6hLC+keOHFmUUCk3dhcvXsT58+fhcDgwNzeH6upqFBQU4JVXXkHV/2fvy6MjK+5zv9uLepG6W1K39l2aGUmjbZgZmIU1BmwMOMSAY3ASE5zYPEOCY5sTk+c4xuvBkGDzEmNI8MnDDs/giTHgBQhLDMbhGKTZta+jdVpSt9Raeu++7w9Rl+qrulsv2ujvHJ1udd1ab91bv+X7VVVVQafTob29XdhDnbRfrh+s/tDjQudj0RCSUSqk6k13Xi1Ch5r84vkiFhLVWN/Xpf3lXwKnTq3tMvTHfwzdzTcjXl2tqV1q+6Q1WFULdUvNSeLJ8s2T7ZfBYBACQWOxGFZXVwWvQjweF7wK+fn5qtrGom9FIhEcO3YMDocDExMTKC8vRzgcxlNPPYX77rtvncdB/J65+uqr8dRTT+HIkSP4/ve/D4vFAo/Hg9dffx0jIyP45je/mRLPP9U4gVSgFI/Dql/8jNHvHZ1Oh/r6emGO7QTlgIBsIGK1WlFbW4va2lrE42uHsLndbgwODgqnOZeUlMBut2+aVyHrOdhYZJWDHYCtoBwEAgG43W7hZNDNeIFsZJ3T09Pwer3C/8vLyzh37hwcDoegGMhBagGTWlR5nk/YqhBYb5Vn9d9oNOLP/uzPMDMzg6WlJVRWVq7b01xpoR4cHITFYsGuXbtw+vRpNDY2orKyEmfOnEF1dTVqamoSFAO1ZYv7yhoTKboAUbzkqD2sWARWvVqQybxy954lqMr1iUXnEX47dw58dzdw7bXg//f/hs5qzZggl6k4AtIuuZPEab67OB/rU6ocqbrV9IvjOIHOUV1djWg0miB4Wa1WYStVOshV7IkR9yEQCCAcDsNqtcLlciEQCMBqtcLtdjPnvVgQJtSiF198EbFYDGVlZfB6vWhpacHU1BSGh4fXndxOYyPpPBuRLmd0qKmpSfCA7zTlQGzE0+neO4QNWIslI7E1Pp8P+fn5QmDzRgZmZ5WDjUVWOdgB2Ozdiubn53HmzBnBDbkV+YrphMfjwczMjPC/2+3G5OQkamtr4ff7k7aoaU0TC4ck3kEMo9GIyspKphVejQXQ6XQiHA6jvLwcdrsdkUgEBoMBN910k+RBUUr9ScXarNPpEIlEhD7Qn6RsJR6zlNdGzJtPV5ulvEhq8ipBzdxISK+sBFpbgbfeAsfY9YklTNO75agd63RRdpKBmJJDQ8nrxKqbpVBIKbFy/TYYDMLptjzPY3V1FR6PBz09PYjH4ygsLITL5UJubm6CZ4gWRnU6HWw2G8rLyzE7OysYI7xer3BKshJMJhOOHDmC3t5ecByHoqIiBAIBoc5QKMT0uiRD56Gft0zPiXSnFxUVrQvY3UnKQTyuvFuR2WxmHsL2+9//HsDaGBUXF6OgoCCja392K9ONxc6Y4e9z0Av3RoLneQwPD6Ovrw+HDx9Gbm7uhtJ6NgPEQwC81/+5uTl0dHTAbDanJPCmIhwC7EPQOI5DNBoVBKV4/L2tHcXcW7FXgiwaBw8eFDipq6ur6Ovrw9GjR4UzG1j1ZmrXGqXFR+5ZoAVG8ViQ+ugDp+h8xDOj0+nW/ZHfU2lzspb7pIQtjgP+5m+AhQXgiScSkuhxAcCcLwRkfsiNi5ISpqndovxyYyIV86GmbClli1bwyA5ErGeJpnmJx4YWnvV6PWw2G2pra7Fv3z60t7cjNzcXk5OT6OrqQm9vL9xud4Lhh1Ze7777blitVvh8PuEMk1tuuUXx2SLpV155Jebm5oQ+1NXVYXFxEbm5udi1a5dkGVJgPVP0e4dcQ0M8RqSNUvNICz0t1XSr1Yqqqqp116kRqLcLtB6CxnGccBGEjaEAACAASURBVADbpZdeikOHDsFms+HcuXP47//+b3R2dmJ8fBzBYDDtbc16DjYWWc9BFkkhFovh5MmTMBgMOHLkCPR6/ZagN2USwWAQIyMjANb639vbC5vNhra2NnAcJxz2JeaCA6lZ0ZUs4bFYDAsLC8xgLS1CuLgeci9tNhvuuusuvPbaaxgZGcFNN92EAwcOSMYF0NZ5uh0seoRSm6SgVSFRAsm7srKCvr4+GAwGFBQUwOl0Ijc3V1bpkAoQJyCCBCsgO1UhWU2fmGhthe5DH0L8P/4DuOkmQDR31LRL7tAtJUWY1CEFufmSDo+CFNJpeZbytEjlNxqNAl0DWNt60uPx4Pz58wDWnken0ynsJlNbW4vvf//7GBoagslkQkNDg6bn/ZJLLkFJSQnm5ubw05/+FD6fD1VVVfjMZz7DpItkIo5AbJhQihMQf5eijKmJO5CDXq9HQ0MDc/7tJM9Bqoeg5eTkoKKiAhUVFeB5HktLS5idnUVXVxei0ajgVSgsLEx5zLLKwcYiqxxkoRl+vx+dnZ2orq5GLbV13k5WDugtS/1+P3p6elBTUyPQA8jCRizPNEjQJG1FZQk+Wvm7RNAYHh7Gl770Jfzwhz9cl65FoJXKx/M8PB4Pdu3aheuvvx45OTmIxWIIh8PCtbSwK3emgJgHzhoDWuEQX0soFlqEUaWxIPV4vV6MjIygqakJOTk58Hq9GB8fh9/vh81mg9PpRH5+fkJ8hZSwR+oi7aKt8azr6PIIxPNGLPCk7FG46y7gtdeARx4BvvY1yWuTKlsmnUVXocum+0f/Tsqm54BYGFRqmxw2m/ICJM4HsgOSwWBANBqFyWTCxMQEVldXkZeXh8LCQhQUFKC5uTlhXFhlsuo2m81oa2sDAFxxxRXw+/0JdKZ09z1ZbyErXfwsKL3P6HeJmjiKuro6ST79TlIO0ukF4TgODocDDocDu3fvRiQSEbZJPXPmDKxWq7BdajJCflY52FhklYMsNGFubg5nz55FR0fHOi6mXq9HKBTapJa9BzUWai2Ix+MYGhpCKBSCx+PB6OgompqahMBeJZ66lIVVzlomxd+lQfLt2rULNpsNp0+fRkVFhZAnHRSmaDSKvr4+WCwWtLS0CALrww8/DKfTiSuuuEKVsCquV42gK6Y5kU+aikB+o5UILYoDqXdqagpzc3Nob28XhILS0lKUl5cjGo1iaWkJHo8H586dg9FoFLjhclv1SgXEiusW95mk0XQSlsIZi8VkLahiyti68SgvB269FfjRj9Y+FbbAlGozq8/JpkuBzAWx4innnWPNFVqAZtHppLCZigPP88jJyUFJSQlKSkrA8zyWl5fh9XoxNTUlUD2Il4s1F1gKOz13dDrdunNPyPzJtFKU6bGly2cppuL8paWlcDgckuVppeJsZWSyL0ajEWVlZSgrKwPP88IhbKdOnUIoFILT6URJSQmcTqcqBSUbc7CxyCoHOwjpForFZY+MjGBmZgZHjhxhBqJuBc8Bi9KSKsbGxrCysoKJiQl4vd4EAZJeWJRoOqy2potqRA4yuvbaa9dRfcTeCrULbTAYRE9PD8rLy1FaWpqQdumll+KBBx5IUA7kkG56DG2JT1bBInmGhoYQiUTQ1taWsEiRenU6HfLz84XD3YLBIDweD4aGhhAMBgXBzG63r1NYpNqXigBOC3taqSv03OA4DviLvwCeew743veAxx4DqHStlIxMC3lanyWa6w4gQUCUajvtnaLTxGOidrzV9Eur14vjONjtdtjtdtTW1iIajWJ+fj7Bq0DOVZDaRYzug9JcE7/T6E+6D6wySX41niIWNloxIYHecthJnoNUaUVqwXEcbDYbbDYbGhoahEPY3G43enp6YDKZBEqd1CFsWc/BxiKrHOwQZEIoJohGozh16hQMBgOOHj0q+WJMRQBMF4iCkq6X9+TkJObn5zEwMACDwYD29namAAhoCwxPdwzCH/zBH+DJJ5/E6urquheo2FtBl0N/0m3z+Xzo7+/Hnj17hL2t6TZdcMEF8Pv9GBkZwZ49e1LyVGilP4mpJ8lSa+LxOHp6epCXlyfwi1n0FRo8z8NisaCyshIVFRXCgVezs7MYGhqCxWIRtgHciJOxtaavmwu5ucCnPw384z9C9+abiF988bo8tPVdLR0u3e1OmUKlwbIMYN1zrXS/1NJVtLaNpEsJ+TqdDgaDAaWlpSgtLRV43wsLC5iYmIDBYEB+fj4KCwslvQpalEAt1DZxHXq9nhl3Q783tShdqaaL6zMajairq1O1hmbKCLfRkKKiZRrkEDYSX+P3+zE7O4uenh74/X7hELb8/HzBOxsMBmV3x2PB6/Xi4x//OMbGxlBbW4uf/vSnKCgoYLaHUOyqq6vx/PPPp9jD7Y+scrBDkG6hmGB1dRVdXV2oqakRTohUasNmIp0KytzcHMbHx9Hb24uSkhKBsiMGi/earLCcrCWtoKAAra2tePnll3HDDTeoKptekOly3W43pqam0NraKryMxTxwg8GA66+/Hr/5zW/Q2Ni4TmhUywFPRkmirbvJKljhcBhnz55FRUVFQiC3FH1Fqs0GgwFFRUUoKioCgIStKXmeR2FhIfLy8lRxo5XS0yEEM+fWzTeDe+opxL/7XeDQoXWnI6sZEylKHfmkqT10uenolxI2yjIt5ZGQ+p2Mh5xXi9BgWMKolOJMeN/19fUIBAJYWFhIiJ0hsQo5OTkb5vEgFDiWZ1XJ68fquxblRE37OI5DXV3dljkN+P0G8SFsXq8Xs7OzuPnmmxEKhfCBD3xA1gsmhfvvvx9XXnkl7r33Xtx///24//778Z3vfGfddRaLBSdPnkxHV3YMdoZvLIuMnHUwOzuLt99+G21tbYqKAWnDVlAO0tEGn8+Hs2fP4syZM6itrUVZWZlAZSFucrG7nCyW5LAynY69vaMad75U3+QUjiuuuAK/+MUvJNOVrPOEOka490QxEAv9pO/XXXcd3njjDQSDQeF31mJPC4fisaDT1YJcn6zAuLKygtOnT6OhoYG5w5McpOgr5C8vLw9VVVXo6OhAS0sLTCYTpqenBU/M7OwsotGo5JiQOrSOSUoBoQbD2tamY2PAs8+mrWx6XMRbf9LPDi1c03ECHMcl7PTEGhct3joxNiKOQKpt5BlijQsZG/qPHhN6LFjPE00fNJlMKC0txd69e7F//36UlJRgZWUFZ86cwfHjxzExMYGVlRVNtLdk+s4qXw2diYyT+E9KsRDPH9Y7h8wrOm95eTlsNptke7LYOOh0OrhcLuzduxe/+93vcOzYMZSWlmJmZgYdHR34i7/4Cxw7dgwLCwuKZT333HO47bbbAAC33XYbnmW837JgI6sc7BCkUzDneR5DQ0MYHBzEkSNHmG64TLchWZCA2VQQCATwu9/9DkNDQ2htbRW45gRy1kAiCLEWNbHwzLKsyi1oSla6Cy64AOfOncPExITwO8/zCIfDitboaDSK7u5uAEBLS4tgpZFbxKuqqlBeXo6uri7Jsuk+02NB2kaPC4Gc8MNa2KXqZWF+fh79/f1oaWlhBh3K9VerMGk0GlFSUoLdu3fDbrejrKwMS0tLOHXqFE6ePCkIZiQPa67QZdNjI/6ToxSqsvBefjmwb99a3MHKStJ9ZqWrFd7F8wWQPk+ArltKEKQVC60W5s1UHEj9BDQtiX5mWGND8tLfydgYDAYUFhaioaEB+/fvR0tLC4xGI8bHx9HZ2YmBgQHMz88L5aZzbGj6Sjq9NWLQYyWldIm9YA6HA6WlpZL1ZbG5qKurwxe+8AW4XC6cOHECn/70p9Hd3Y3rr78el156Kb71rW9JPktutxtlZWUAgLKyMszOzjKvCwaDOHjwIA4fPpxVIN5Flla0Q2AwGNIimEejUZw8eRI5OTk4cuSIJppSOik9ySJVz0EoFMKvf/1r+P1+tLe3r3NlyvXRYDAk1X81FBkpygZpE1n8r7nmGvzqV7/CZz/7WQDAM888g+7ubnzlK1+RrF8ceEyXq9Smq666Cq+99hquvfZamM3mBM5+svQYgH2OAV0vi07B+qTLIwHlHR0dTBd1Kt4INQI4CSIF1sacbJ0aCoXgcDhQWFiI/Pz8dc9cKtQV+n6IQeZdLBYDOA74/OeB225b273ozjsV+5wxmpNCmrhslieO9ItWKMTKuBTfWomyshGKA50uVvy0jCtrbEi60WgUYhXi8TiWlpaE7XsNBgOcTicKCwuFGCaxZ0LL2NBKXCqKR7rTTSYT6urqJK/PYmtBr9fj8OHDOHz4MO677z54PB5cddVV+MlPfrLu2m9961uqyx0fH0d5eTlGRkbwgQ98AG1tbWhoaEhn07cdssrBDkE6rParq6vo7OxEXV0dqqurN6UNqSIVz0EwGMQzzzwDs9mM5ubmdQKmGmE5GWEnmRgE2npKxjwWi+HgwYP46le/Cp/Ph5aWFhw4cAAPP/ww7rjjDhQUFMBkMiWU4/P5MDAwgN27d8PhcKjmxhOUlpaiq6sLX/7yl1FZWYmPfexjqK6uzpiQTSAeEzkFKx6PY3BwEDqdDm1tbYJAyBIW6XtOyqKFIhaUBBKWp8NsNqO8vBzl5eWIx+NYXFyEx+PByMgIzGazIJhZLJaUBE2lvAnPa0sLuGuuAX78Y3A33wy8qyjSlCcxFz7ZdqViSNAinLM8KnR+Vh+kuPx0efR8YVn209H2jUzX6dZ25CooKADP8wgGg1hYWMDw8DCCwSAcDgcKCgokD7NSUs6J92IrgeM41NfX75jTjrUiWTreZkAqntLpdOLEiROS+UpKSjAzM4OysjLMzMwIAdBikB2q6uvrccUVV+DEiRPve+Vgaz2tWSSNVAVzEl/Q3t6elGKQjjakA8kKHT6fD//5n/8Jl8uF2tpaYWcNWjAC2Px4NVbOZBQDJdB5OY7D/Pw8XnvtNej1eng8Hrz11ls4duwYbDYb7rnnHnzta1/Da6+9Jtyj6elpDA4OoqWlBXa7PcFiKkfXIDSNmZkZvPjiiygsLITf78fS0hIef/xxBAIByTYnqyTReVllSOWNRCI4c+YMcnNzsWvXroR7qcSJl2ozayyk4gTIvZdTLHQ6HQoLC7F7924cOHAAdXV1wvkSnZ2dGB0dhc/n08wLl4OUkMrfeSd4AHjkEVkuPN1P8TxREyeQLiqS2n5pqZs5Lnzinv80H57+lBsXMVVOPC6S9+TdcjdCcSDjbjabUVZWhtbWVuzfvx8ulwvLy8s4ceIETp8+jcnJSfj9/nVtpMeD/iMByWIPBqmXHg+5eZPse5aVXlVV9b7eGjMe3z5bsgYCgaTu1R/+4R/iiSeeAAA88cQTzM06FhYWhPOZ5ufn8bvf/Q579+5NrcE7AFnPwQ5BsgHJJL5gdnYWR48eXWdZ1tqGraAcaG3DzMwM3njjDVRXVyM3N1eS781aWMkCJl7oaCRrcdYiSOt0OvT19QEAmpqaMDY2hssuuwyvvvoqCgsL4fF40Nrail/+8pcoLS1FTk4OkzqlREmg6+3p6QGwxgkdHBxEU1MTZmZmMDY2JvlyTZZqJFaExEIGKy85ybq+vn7dgX2s/qptl5ziIG4zbWkWzwsx95n8Rk7GraqqQjQaxcLCAmZmZjA4OCicjOt0OiXbTOrW6o0CAJSXQ3frrYj/6EfALbcIB6PJlS2eJ0p0IVrxFINWPtRa9dViM+hA9KfSXBO3lVaGicIl5cVKlW4j1zedTiecm1BXV5dAiSNeBZfLBbvdLmuFF99v0gcipMop0aR9Up4Jeozp/6X653Q6hR3GtIBuw3ZHPJ6+05EzjWTPOLj33nvxx3/8x/jhD3+I6upqHDt2DADQ2dmJRx99FI8//jh6e3txxx13CHPk3nvvzSoHyCoHOwbJCObRaBQnTpyA2WzWHF+QrjakG1poRTzPY2BgAENDQ6ipqWFuY6eVH09bnaUWXFowklrk5JQcVps4jkM4HBZc5YFAACsrK4hEIqitrcXQ0BDC4TBMJhN+9atf4aMf/ShaWlo0LXTieo1GI3ieh8vlEtpOBBlx++TGgqRL0afE9aoRshYXFzE0NITm5uakT9VMRVgUt5nljVAqG8C6k3HJSc2Tk5OCx0G8h33KAvTtt793MNoPfqC6z2rS5WhJSkoF3T9WuanEG201ug89PqRPcnNNStmi87EoViS/FsWCpsTFYjFhTg4PD8NkMgmHApL96WmFUE35culyMRRyigX9aTKZkvaObydruxI26gC0dCDZ05GdTideffXVdb8fPHgQjz/+OADg6NGjOHPmTMpt3GnIKgc7BFoF85WVFXR1daG+vh5VVVVpacNWsKioFRCIYhSNRlFSUpJU25WsbVJprAVOnJfugxI3nghG9fX1OHfuHABg//79mJ6ehsFggN1ux8UXXyxQj5qamlBfX7+uXq2Un/b2dvzqV7+Cz+dDdXU13G43nE7nugA/pbFgWdCl8koJibTFcGZmBtPT0wknWavtE11epjjzqQiS5JTR2tpahEIheL1enDt3DoFAAPn5+XA6ncjPz09Y9MUeJsV222zAZz4DPPgg8OabwLtCXqoCsJLwr9WDI65bbg7RcSZynolk6s6UYhGJRHDy5EkMDw/j0KFD63ZN09I+FuWJTpPzdsqNlV6vF85NANboH16vF0NDQwiFQsIBbIQmxILSfUiVG08rDuQ9mayAv9OUg+3Sl+zpyBuPrHKwQ6BFOXC73ejt7cW+ffskF5ztCjWeA7/fj87OTpSUlMDv9ydFv8iUYMlKo5UJqTZxHIeysjLceOONeOmll7CwsICamhoUFxdjcnISeXl5mJqags1mwwc/+EEmj15rf/Lz83H77bfjl7/8JUKhEA4ePIirrrpqHU0pXdZ38VgAiYIvz/MYGxvD6uoqOjo6Es6bIOWx6qfLUqMkptOjoLVs+r6ZTCaUlZUJZ3AsLS1hfn5esOAS+hE5r4KUTVOdSJnr6rjpJuCpp8B/73vgvvSljFvW5ZBK3SzPE/ldnF88LqRu2vKtlSqUbNsXFhbwpS99CfPz8wiHw3jqqafwd3/3dzh06JDqvsuli9uv5j0nVihohZw8R1arFRaLBRUVFYjFYlheXsb8/Dw8Hg94nsfU1FTCnFQzfkpxBFr6X1tbq/mUXRrbiYqjhO3kOcgqBxuPrHKwQ2AwGBAOh2Wv4Xkeg4ODmJ+fx5EjR1KKL9iqUFos5ufncebMGezduxdut5tpNaMXTNbilCmrcSoxCEQQPnDgAPbt24dIJAKTyYRQKITnn38enZ2d2L9/Pz70oQ8JFBW6TSzBCMA6IUCMiooK3HDDDdi9e7em9pJ6kxlHUi6dNxaLoa+vD2azGS0tLQl9Egt0chQnnufXKRVi0AKneLyUhDE5pCJg63Q6FBQUCMq+3++H1+tFf38/otGoYN212+1Cv+hxWVe2wQB87nPAPffA9dvfAocOyVJXUokTyKTiQNqmpm7WPKe9WlJKOf2MiMdAyVsi1fann34a09PTwta2PM/je9/7Hn70ox8J9MfNoDrRnyy6Dw2j0YiCggIUFBSgqKgI58+fB8dxAsXR4XDA6XTC4XBIKu7pbH9xcbHqM3uksJM8B9tJ0fH7/UnTQ7NIDlnlYIdAyXMQiURw4sQJWK1WHD58eMe84MSQohcQq/LU1BQuuugijI2NIRKJCGniMqSER7JQS/Ge5fi1SQeJqsgLvGdF1+v1goA7NTWFlpYW3Hjjjcy9/aUEALpsubFQQ0vQ2h9SvpwiROcNhULo6elBaWkpysrKUlLA6LLlhEHynVxH0ybEY0Hv3rMRHgUAsFqtsFqtqKysRCwWw8LCAtxuN4aGhpCbmyvEKhiNRumy3z0YrfIXvwB/xx1AXp7imLDaLRaeCaSs+lr6LYdUlVMtbZPiwrM8FmSuSLWP53mcPHkSFosFy8vLWFxcREVFBYLBIGZnZ1FRUZEy1WmjYyxisRgMBoMQq8DzPLxeL+bm5jA0NASz2Zzg6VJ6zwLy2/SK+5ebm4vKykrJ69ViO1FxlLCd+rK6upr1HGwwssrBDoGcckDiCxoaGtLygtzK0Ov1gtBPEI/Hcfr0acTjcRw+fFjYZYMFpUVPTgEjiz5tkRHHC9AvY6XYAzVtoi2X9DVkK0ybzYa9e/cmFYioZiyIBV98HStWgP4UL/yyVmxRm2msrKygr68PDQ0NKCgoUB0Qy0KyCotYOZOqU248xN/VjoeadhsMBrhcLrhcLvA8j5WVFXg8Hpw9exY6nU6IVaCDmt9tEHRf/CLwZ38GPPEEcNddzL5rsYwrUdnEz0uy84S+PhNzP9l0+nmVe5c0NDRgenpaoAOGQiHodDq4XK4EpZxA7btEfD0LmVA8WAqi0+mE0+kEz/NCrEJfXx+i0agwJ2lPF10+y4hBp9HjbzAYUF9fr4oyqISd5DnI0oqykENWOdghkNrK9Pz58+jr68MFF1wAh8OxIW2RWpA3AmLPQSgUQmdnJ0pLS4WA3eXlZcm8qdKFaA47oN06Kl5A6cVOTgCgxzsYDKK7uxvV1dWy2/Wl4qmQ41zLxU3Q35UoKHKceADCdopkR6JUA2JTiSPQOpb0GKhpl5bYCTkBnOM4Iai5rq4O4XAYHo8H4+Pj8Pv9sNvtwknNOTk5iDc3w3PhhXA++SRw003CwWhKY6IEqfGm55WSIk576FgeHXJdutqmNj0disWtt96K48ePY3V1FUajEUtLS7j77rsFKqjWsaEhRbfLJORoehzHJXi64vE4vF4vZmdnBa8C2UpVKl5A/DzR41NbWyu7MYEW7CTlYLvRirLKwcYiqxzsEIg9Bzy/tk2nx+PB0aNH0/ZyVNsOFoVlo+onC+/i4iJOnjyJvXv3ori4GDMzM/B4PMx8qfD9xQKtnGAsl5e+Vo1SQS/+BoMBPL+21eXg4CD27NmTcOIxy9Kmpj9KEJeTzngMFseZfPf7/RgfH0/YkUgqboLkJQKTlrFItU/pos2whDk17ZYTyoD3tkotLS1FPB4XtqUcHx+HwWBYOyPjhhvgPHlybVvTr31NVbs3asyU6DwsIVoNNVBcpviaZNuutm+VlZX4/ve/j9dffx0vv/wywuEwPvKRj2gadyllkeflA5CV5kwyzwrJo6b9ABI8XXT8TDweh8PhQGFhoSqvQllZGex2u2R9WrGTlIPtRivKxhxsLLLKwQ4BrRyQ+ILc3NwNjy/YbOWALD5TU1MYGhrCwYMHkZeXB6/Xi5mZGcUgUyVrtlKamA+frBCuVWDleR6hUAhDQ0NobW2FyWRilk33nyVEywkOrHppi3Wq1nc1eePxOEZHRxGNRnHgwAHo9XphrKQUIak4FFKv2NtDoMayqvYeap1XWspWyqvFQ5Ofny8EwRKqx4rNBvcf/AFKf/UrLF1/PWwXXphRy7kckpljYk+C2nFhlSEVc0I+lbxAWhSLwsJCfPSjH0VVVRW++MUvIhAICGcHsJBOKpTasdFCAzMYDEndO3IoYE1NDcLhMBYXF4X4GYvFIngVLBZLQn6bzYby8nLJ+pLBTlMOtpPnoKysbLOb8b5CVjnYISBC+fLyMrq6urB7925UVFRsSjuSXfjTAZ1Oh7m5OaysrODo0aMwGo1YWVnB2NiYpOCrxGEl5dIgZbEWMzVWsnRb2EdGRhCNRnHw4EFFxUyrwCm2xtNjoUR3ostINRYgGo2it7cXeXl5sFqtqhY2NVQjOcVBaV6QOsT9EFuyWWVvJQGabifJT7ZKnZqagvNv/xaxt96C/p//GZ1//dewWK0CZzwnJ2ddH8mY0PEWRBHbav1Wk86KcZCj00nFlIjnhxpKj9VqxWOPPSarGGQiTkBNOt1+tc+3FN0JkH6fkPrF8TOrq6tCrEIsFkNBQYEQ2Mw6yyVV7CTlIEsrykIOWeVgh8BgMMDv96Orq2tD4wvEkLPSZhqRSAS9vb0AgIsuuggcxyEUCmF4eFiz9V5NwCPLikjvTEN/aqELaVEqSOBxbm4uTCaTcGqx1nLlINdmoiSxxkJsbZWypKvxrpA4iqqqKhQWFsLn8yn2KRMCuFYvCT0GchQILdQspfRUKFJS6Yb8fOB//S/kPvggDgQCWG1uhsfjQXd3N3ieF07FzcvLk1SGiOAnJxzKIZOKQ6pzRZxffF+V3ov02LBoTXV1dYp0p60MubEBlL0q5BrxnLHb7cKhgOFwGF6vF+fPn0cwGEQkEkFJSQmKi4vTtm33dhKolRCLxYRtcbc6sluZbjyyysEOAM/zGBoaQiAQwNVXX71h8QUsaD2pOV0gOzJVVFTA5/OB4zhEo1EMDg4yA7WB1ARL8WImtqDJlUt/lxKQWIKAuE1EYK6srERJSQkWFhZkKQ2ZoPyIlR/6u1pFSCpWgJSzvLyM/v5+7N69Gw6HQ9glKZ3eFzGU6CHJ8L5pq7IS9UQsJNJjo+ShycQcAADdxz6G+FNPgfs//wd5Tz2FvJoa1NTUIBKJwOv1YnJyEqurq8jLyxOoHsSLpRSLozT/lLjw5HmXmkNy0Er3ESOddB5gfZuJAi7lxRIrXaxyMqEwakmXu3fpojsZDAYUFxdj//79KC4uxtLSEtxuN9555x3E43EUFxejpKQE+fn5mhVTgp3kOYjFYikdCLeRyG5luvHIKgfbHJFIBMePH4fNZoPVat1UxQDYHOVgdnYWPT09uOCCC2AwGAQheXh4GKFQiJknnXx/Gmr6TwuMWizGpG0cx2FxcRGDg4PYtWsXnn32Wdx2221Jc51TGQu5/iYTNyHO73a7MT4+jtbW1oSTfukyxFBSSjJJ6Umn1V/8XQ0diP6k86qxyiq2GxAORsOzzwI33wxg7bCrsrIy4XA9VlCzy+WSpMWoUcSVrO6xWGyd4k3SSFyKWgVLCzLtkZCKhwHemxNqdi6i2yP+lFMs0qU4SFnc062Y5Ofno6SkBADgcDjgcDiwZ88eRCIRzM7OYnR0FD6fD3a7XfAq5pWmCAAAIABJREFUaFkzt1MQrxK2kxckSyvaeGSVg20McXzB7OzsZjdpQ5UDogC43W7hxOdAIIBYLIaxsTH4/X7ZAORkoCRIK1nZk41BoAXtmZkZTE9Po6WlBWazGf/1X/+FmpqadS96cbAgDbX0GDnodDpJr4yavEr9HRsbg8/nQ0dHR0IcBWmzlrEUjwFLUOR5XnH+ZtIyn2zZarwoSnx4+n8x7SOh7ssvBy64AHj0UeCaa4C8vHVlE6EMWPNuLSwsYHh4GMFgEPn5+cJWqWqErGTHVOyxUZoraqlO9LVqkIpHgqSzhHct+VntUatYqKGBSdGdpBSTVNovl24ymVBbW8u81mg0oqKiAhUVFeB5Hj6fD263G2+//TZ4nkdxcTGKi4sVvQo7zXOwXfqSVQ42HlnlYJtiZmYG/f392L9/f1q3aksVqVhdtSAWi+HUqVPQ6/U4cuSI8JLT6/Vwu92SXEqWAMZa/MTCoxrBkeRj9T8d3HgSeBwMBtHe3g6DwYBAIACXy4X7778fZWVlGBgYwCc+8QlYLBZFC7qSVZH+ncWhJoJSuvsLAL29vdDr9WhtbU1YwEhbkokhEcc9sPISaooaYVGtgqlVeNeKVPnwSh6eBAFRpwO+8IW1g9F+9CNwf/3XsnktFgvMZjPKysoQi8Xg8/ng8XgwMjICs9kMl8uFgoKCpDjhap8bqXsoRf9ipdN1ir9Lea8ItCoUYkjlT5ZeRtKTVSyUyqefH5p2aDAYEjwhqY4LDZ1Oh4aGBlWWcI57b1euxsZGhMPhBK+Cw+FASUkJioqK1nkVtpO1XQnbabei7FamG4+scrDNwPM8+vr64PP5NvT8ArXYCM9BIBBAZ2cnKisrUVdXl5Dm9XoxPz/PPAlaakFTY0WnrWxSrnlgrf9KFjSp+qXqjcfjQuBxXl6ecOIxx3F47rnnEIlEsLi4iN27d+P06dPIy8vDxz/+cc0CutiqqEQ14jhuXQC2OJ2liMn1NxqN4uzZs3C5XJpP805FACfjIWU9V8pL10EjHo9jaGgIDodDsu8bFf+QTDpzPJqbgWuuAffjHyN+003AuzQOcT6x5Vmn0wk7zcTjcQQCAczNzaG3txfxeFzYacZutwv5k1WYaKu7XLoUUuXB0/dMrFCQP7lYErp9LM+B0nO0mWApWvRp6kCiAkHHI6j1ZonvT1VVlexuTnLIyclBZWUlKisrwfM8FhcXMTs7i5GREXAcJ8Qq2O12xOPxbRPEq4TtpOhkPQcbj6xysI0QiUTQ1dUFh8OBQ4cOpc3qkk5kWjnwer04deoU2tra4HK5EtKWlpYwOTmZVP1aBGmlhYr+LhdwS5cnJzQGAgH09PSgqqoKxcXFCde88847KC8vx9TUFObn59HS0oJ33nkHt956a8Ys0aTN5JOmbchRFaQsrWR8VldX0dPTg9raWjidTk3tSlXYk4MWyzx9H8nWq3a7HdXV1euEP/qTNSbisrUio4rDnXcCr7wCPPKIcDCaGEqUFYvFgurqalRXVyMajWJhYQHnz5/H4OAg8vLyBK8CvQOXWi48jWSs7pmKIyBzXW2cAHlv6HS6dXOEVhBoxXYjAoyTSZdqn9gzqbZ8Up7T6Vy3FiQLjuNQUFCAgoICNDY2IhQKCSc1Ly0tgeM4uFwulJaWbnslYTt5DrLKwcYjqxxsEywtLeH48ePYs2eP5MEu5KW5mTzCTCoH4+PjGBsbw6FDh9a9KAKBgGDp0WqdTafgKF7YWUqFUr20IiE+8ZhGPB6HxWJBNBpFc3MzFhcXEYlEYLVak7ZEa7Vii62iajnUYpAA66amJuTl5UlaE8lvOp1OkuustU+ZUDqCwSB6enpQWVm5TqEjbdZatpjuxKIFqbUmp6w4VFYi/id/AjzxBHDrrUBTk6p6peo2GAwoKipCUVEROI6Dz+eD1+vF+Pg4dDqdsHe91WqFwWBICEAWC//iZ1Cr90qp7RupWBDlm3yqEbzpZ4cFmmKnVH+60okwnw5PFq2IWywWVFVVSV6fKkwmE6qqqlBVVQWe53Hy5EkEAgG89dZb0Ov1QqwC8XZtJ2ynmINQKJS27WizUIescrANMD09jYGBAcX4AiKYb+YDn0qQqhTi8Th6enoQCARw9OjRdYd8RSIR4SwD2spGFiS5BVnNYq5FkKY5tXJQWgTj8ThmZmZw/vx5IfCYts6T7x/84Adx7Ngx2Gw2AIDH48Ett9ySMAdoz0SmrO9KQpNcXtLPtrY2YQEQC7/ivLSSIaZoiKkaRFhSyytXC6m8Kysr6Ovrw549e5KOB5Kifam1nCt5rOTiL1QLcLffvrZr0Xe/uxagrNJyLQfSJrvdDrvdjtraWoRCIXi9XoyOjiIYDMLhcAhBzWIan/j9QxtLWFQnFpJtuxoko1jQ9zEZDxadLkV1Ip9kjKTanKzio8YjoNVLptfr0dDQsGHrHcdxMJlMqKioQHFxMYLBIGZnZzE4OIjl5WUUFBSguLgYRUVF28KrsJ08B0rPbBbpR1Y52MLgeR69vb1YXl7GxRdfrPjC0ev1iEajm/pi0uv1CIfDaSsvHA6jq6sLTqcTLS0t614QhNNNb1lK01zECybLGp0Mz1zOgkeUkmSt8zzPC31qa2tLUIbEeS+99FJYrVa8+eabAIAbb7wRBw4cYJYvdseL+01zobXETSi9tOWChEdGRpj9pMvWyv1Wa1Enp3krWVlZkGqXx+PB6OgoWlpaZDnQmVK0WOlqLee0IkGPCVG2aQoLACAvD/jMZ4AHHwTefBO49NKMBF6Tk5rLy8sTgppHR0dhNptRWFiIwsJCVR4zLdt+kjz0J/1dK9UpWY+FlGC0tLSEt956C5FIBIcPH0ZRUZHmskn5BErtp7+z2iRFdaK/Jwvx+NbW1m64NZl+X5jNZoEWF4/HsbCwIFCQ9Hq9sFWqzWbbkoJtPL59Yg6y2HhklYMtinA4jOPHjyM/P1847VcJm3UAWabaQKhUTU1NKC0tZV4zOjoKv9/PTFPitqoR4OViBcRlknxSMQSsNokRi8XQ09MDm82GhoaGdZQalvBy8OBBHDx4EKdOnWIqUOK8LIFZTginqTxiiK3yYkiVSwdYNzc3KwoaUu1KxUJN5qkW67nYykpjamoKbrcbHR0dsgr6Vo0jkFKkiLLNpJTdfDO4p58GHn4YuOQSoQ5WeelQHHQ6ncAJB9a4yF6vFwMDA4hEIkJQMwkAp9uaTN1qYz/o957SO4MuV6l+cq3YQzI6Oop77rkHwWAQPM/jsccewze+8Q3s27dPU/+STRe/4+QUK/qadNGdyGFmGw0pz7xOp4PT6YTT6URzczOCwSDcbjf6+/uxsrKCwsJCwavAMoJsBraT5yCLjcfWmKVZJIAIxY2NjSgrK1OdbycpB2q2ap2YmMDi4iIzLV10IZagL2WR5jgOBoMBoVBoHa1HyiJPg5x4zAo8ViPcSF2TKl1IKa/4fstZW4H3+lleXi4cWKQVqcYRJKt0sOgRtAekvb094d6LYwRYMQPpojllUnFgged5QK8Hf/fd4O65B/x//ifwsY8xryVeGrHgLKbMaKU6Wa1WWK1WVFVVCbt2ud1uDA0NITc3N4GOJ4V0xAnQz4AawZkuWxwvwBof8Zg88sgjwmnUPM8jFArhoYcewhNPPMEUyjM5L7TQheQ8muRaqU/yXOXm5qKiokKyvkxCydNIYDabUfPuCeLEq+B2uzEwMACj0Sh4FfLy8jbNq5AOb04WOxdZ5WCLgSgGBw4cEHjkarETlAOe5zEwMACv1yu7Vevs7KzkoW+pCH+pUAPIizYWizH54izLKxE2FxYWMDQ0hMbGRkEZoq9V0x8p612mrO9K1lb6O/kkfPzdu3cnBFgr0RTUejnk2qUGWsuOxWLo6+uDxWJBc3PzOi+K2FOlZH2W81bJ5U83FUlT+eRgtMceAz784TW6kSivWHiWSxensahOdDlkXAwGg7BVKs/zWFlZweTkJHw+H06cOIGCggI4nU7k5uZqEoqSiRNQmw6sF5hZnkhxmYODg7BYLFhaWkI4HIbT6YTb7UY4HIbZbE6btybVOAH6+WUJ1VL5pbxYBoMBdXV1mypQa41xoL0KwNrmGbOzs+jt7cXq6ioKCwtRUlICl8u14V6F7aAcRKPRrIdjE5BVDrYYbDabqvgCFsguHpuJVASzaDSKEydOwGKx4NChQ5IvYZ/Ph+np6YR0sdVRrXuaRipCJ01DUgoGJCD/i088VuI9S/VL64s+FYEwGaFifn4eY2NjTD6+lmBbcg1NXxHzwLW0i0CrgB0Oh9HT04Pi4mKUl5enXLacAM3y0JByySfr/pNxTVVAlBWQdTrwn/888MlPru1edNddktey2p+q1V5MHSS/OxwOxONxYceZhYUFTExMYHV1FXa7XYhVkBP2ko0TUItkA5QbGhrQ09MDs9mMxcVF5OXlCYd2iWNupN4btNeG1RY1io3asZF6HytBPP719fWbGlOXjHIghsViSfAqeL1egYKUk5MjnKuQJ1Ky368IBALZbUw3AVnlYIuB47ikX37b2XPg9/vR2dmJ2tpaVFdXy143MjIiuWgS9zOxVGlVEKSgVqlgXacmILe9vZ1pHVEbcCtuB8krZ7FL1tKsVWDjeV44h2Hfvn0J+9ZrqZduN+HB03VIUbfEwhHLAq0k5Ij77Pf70dPTg/r6ekHA3Aw6EIvmxCqfnjP0J62Q0f9rtjzv3Qtccw3w5JPATTcB78YIpSJcJ6M40O0nChXP8zAajcK2k/F4HEtLS1hcXMS5c+eQk5MDp9OJwsJCWCyWhDFKhuqkNj2Vsbnjjjtwzz33YHFxEfF4HB6PB3/6p3/KVABY30n9Sh4bKYWTXKO2/ywKi9bxKy8v1+xNTzfi8fQG8ep07x0MCKy9V2ZnZ9Hd3Y1AIJDgVXi/Ws/9fn/2dORNQFY52EHYrsrB/Pw8zpw5g46ODhQWFkpeFw6HMTQ0pMp6TwLHpARpVl6xJY1AjfAoboPU/wTkgCybzSYZkKvVEi3m7oqVCjqvVGwCKUesVNBClxalIh6PC/eMKEBytKxM0IXUCNByvGe6fcDamQz9/f1oamqCzWZLO5dfXGc6aSEsBVNpjtF8b1bbhLl4113Aq6+uHYz29a9nfFzUWt1ZQinZCrW2thbBYBDz8/MYGBhAOBxGQUEBXC6XcG/F5dKfSlQnKaQ6No2NjSguLobH44HRaIRer8fjjz+OCy64AI2NjRmnC0l5bFhjDWDd+0Rr++x2u6b4u0whHZ4DOVitVtTW1qK2thaxWEzwKvT29sJsNgtehfeTsLy6upr1HGwCssrBDgLZynSz26BFORgdHcXk5CQOHz4su/VjLBbD0NAQIpEIM51eTAh3m0CrlVyJ80vKZH0S6w5RMlgLIDnxuLq6WnL7wWQEJzqGIRUhWu7+sazQNMWH/M/zPCKRCHp6euBwOFBdXb3uvkiVy2rX66+/jmeffRZ+vx9HjhzBnj17VOdPxtNBf9Jlu91uTE1Noa2tDWazWVapVFO3Urs3LY7gXUjRkpj9KisD94lPAE88Ad2f/An4d2MwxOWRtmndVjQZSD27dNlmsxmVlZWorKxENBqFz+eD2+0WeP3Eq0AoO+kUnFncejX3dWBgAGNjY8IhiAaDAeFwGD/96U/x1a9+NaOKCStd7LGRi6OglU4pqhHtCczJyUFdXZ1kezYSmVYOaOj1euFgQGDNgu52u3HmzBkEg0E4nU6UlJTA6XTuaK9C9nTkzUFWOdhB2CqeAzWLejwex5kzZxCNRnH06FHZlxuh3wQCAWY6azFO1tJPQ04IkBPCyT0Qt4njOCwsLAgnAYsDj9VSOZTiGpJd+JMVosUUH+C9HYmIAkQL0aQuuhy5mIF33nkHP/zhD2G322E2m/Haa6+hv78fF198sWKfpMqU6pNUOs/zOHfuHJaXl9He3i4EDkoplSSvUpwA/UmXoZXmlGy/5MqXa4OkInf77eCefRaxf/qntQBlCY8Yve0n/Sm+LhnhmUW3UwsS1Ox0OsHzPFZXV+HxeNDT0wOe54WgZqldZpSoTmo8HmLBWax88/xasDW5NhgMwmQygeM4gWYkV/5mpIuFarl5LjZA1NfXb6ntPzdKORDDarWirq4OdXV1iMVi8Hg8cLvd6OnpgcViEbwKagRpFs1rqyKrHGwOtsYTl0VakO4DyJJtg5KCEgqF0NnZiZKSknV7+bMwMTGBlZWVBGGBvNxYi5F4z/Fk+e1ykMpL2iOuk/Du6X3wWfmlLNH0b1LjqxQ4ms5gXFZe0l6fz4fBwUHhhGAlS6Jc2TqdDi+88AIsFgvi8ThWVlbgcrkwODiImZkZlJeXp2SZVyNAx+NxDAwMQKfToaWlRRAOki07nTQnlpCVTsVBSXhbh7w84I47gAceEA5GE+eV89KoDY6WE9DEPHt63LSOe15eHvLy8lBTU4NIJIKFhQVMTk4K24g6nU4UFBSkVXgVjwmtfJOx37t3L4xGI1ZXV2E0GhEMBmG1WvGhD31I0luTDvj9fkxNTWHXrl2a8pF7plVprays3FIUmo30HMhBr9cLMTTA2i5ws7OzOHXqFEKhEFwul+BVYLV3O51xsLq6uqXmwPsFWeVgB2Er7FakJJiQbQX37t27bi9/Fs6fP4+5uTlmPVJ8VvLSo2MQ5Pj5Uv1IRqlgCejxeBwjIyMIh8Po6OhQFGykrGpSioFSrEAqVCNSrlxe4i3S6/UC7aa1tRVmszllQZW0n/R9eHgYhYWFMJvNOHfuHKamppCfnw+n04n8/HzmgkfuJUthU2pXNBpFd3c3CgsLUVlZmTDWGxVHoEWAppVKKcu2Wq4+2aaVBEuqzc/feCPw1FNrB6MdOQKoFJy1WKVZbWCNCz0WrDgBJToMDZPJJAhkPM9jaWkJHo8H4+PjgsehoKBA0sqZTm9OTk4OHnjgAfz93/89lpeXEQgEcN111+Gqq66SfTfRFmPaW8eaK6z3z/DwMO677z4cO3aMSZNKl0IMAAUFBarWiI3GVrS4EyW2vr4esVgM8/PzmJmZQXd3NywWC0pKSlBSUiJQd8n7ejsg6znYHGSVgx2ErUArkntxTk1NYWhoCAcPHlS1TdvCwgKmpqYk02mBT7zo0NY2sQAgZX0UWxxZUBJgxLSqaDSKnp4e2O127N69WxWlgAWlhZeMO+uMBXGb6Xsk/s7i2yst6MDaeE9MTKyj3chBrTB05ZVX4rHHHkN+fj44jsPExAQuvPBCHD58GLFYDIuLi5ibm8Pw8DCsVisKCwtRVFQku/iRulmKGplXYmqU2nZnykOjJh2ArAAt1SZSNplLkUgE3d3dcLlcqKioAM/ziu8XoW0GA3D33cA99wDPPgvcfLPqtstBrVIjlSdVT434N4fDIZzVEQ6HMT8/j5GREQSDQeTn5wtBz8lYzNWkt7a24mc/+xlmZmbwne98B3v37pU0PLC8QVq9TTzPo62tDYFAAKOjo4L3QE0chhJYcSA1NTVJl/d+hl6vF5QBQo1zu904ceIEIpEIXC7XuhPEtzKyysHmIKsc7CBsBeWABZ7n0dfXh6WlJRw9elTVVq2rq6sYGxuTTJcTsqQ8KDQnX60QzhIUaIubmB4DvCeEkO0ua2pqBGujFNIRC8DyWrDGSYsFnZQhXkjE/OmBgQGYTCa0trYmjFmqlB4AuOSSS7C0tIRf/OIXKC0txYUXXojPfvazANbmPDlgiCyEXq8Xp0+fBsdxKCwshNPphNVqZVr9pahhS0tL6O/vFw5rE1ugWYplqh6azYojIL+RZ4YoRTU1NcKBYrTXSo3wzF9+ObBvH/Doo8A110Bnt2c0BkIJWhQLloKslN9kMglBzbFYDD6fT1AWLBaLcKaCyWRal19N36XS9Xo9qqurcc011+CVV17Btddem9byWelXXHEF/v3f/x3XXnstLrjgAoHyJ85Df5K2Sr07xe2tr6/fNpbtrQyaGtfQ0IBoNIr5+XlMTk7C6/Xi7bffFk5rltsQZDOR3cp0c5BVDnYQtsJuRWJEIhEcP34cNpsNF110kSprRSgUUrVlKQuk/GQst0q7cCjlJdZVYG27y+HhYTQ1NQmHMdELo9r+KEFs8dQiQGkRyFhKRzweRzgcxsrKCqqqqlBTU7NOKBDfbzVWbZaCdt111+Haa68VxliKC2+z2ZCXl4fq6mqEQiF4vV6Mjo4K1tyioiLmFpV0GXNzc+sOa1NjHVWyPovvj5Z7tVGKg9QJ1qx2ywrPHAd84QvAJz8J/Y9+hPhdd60LSidlZLJvUpSZdEHK25afn4/8/HwAa8KNx+NBb28v4vG4oLCSeBwpKqC4fKn64/E4Lr/8cnznO9/ByspKgldWjUVfyzwcHx/H66+/jrm5OXR1dcFsNuOhhx5CbW0ts0xasZRSCMQng9fU1GxZQXW7w2AwoLS0FBaLBTqdDrt3707wKhQVFaGkpAQFBQVbIrYCyG5lulnIKgc7CFvNc7C6uorOzk7s2rULFRUVqvIQXnksFtMcK0Cul7omFeu8FqXC7/djdHQUra2tMJlMkp4KYoEmC6hYaFJql7hellCdDss9Ky+x0vf29gqcVtJuLWPJEqLJPWQJXWp3wwLWOOJlZWUoKytDLBbD8vIyZmdnmVtUkj6Pj49jfn5eCBpXCyXrM71Djxi0wiO1IKdi+VUrXHu9XoyMjGDv3r0Ji7GSgCqZtncvuA9/GLEf/xi48Ubw7x6MJva2qbE60/FF9KcapUcOmfZYcBwHq9UKq9WKqqoqRKNReL1eTE1Noa+vDzabTfAqSFHxyLtBri82mw0HDhzA66+/juuuu05T+7Qo6g899BBCoZCQZ3l5Gf/0T/+Ef/7nf1aVn5VOPxfkmcwisyAByTabDTabDbt27UIkEsH8/DwmJiZw+vRp5OXlCV4Fs9m8aW31+/0oKCjYtPrfr8gqBzsIW0k5mJ2dRU9PD/bt2ydY0JTA8zyGhoYktywVW5hY+QH2gpTJnXpoisro6Cii0SguvPBC6PV6xcWRvl9KipBYWKKFSbFSlEneO7AWD0I8IzT9S6uVV8ozw2qf2PJMe2KkvDIEBoNBsOYSxcbj8aC7uxscx8HpdGJlZUXgVYspDZkcT1rhkVIipeolf1KWfbWKw/nz5zEzM4P29nZBWVLTdkXh+c47gVdeEQ5GE+dVihOQK5t+H5DyWOVIjV8m4gCU0g0GgxDUzHEcfD4fvF4vJicnodPpBOHYarUK/SMWd6X3w9VXX42XX34Z119/vZDO8pyoMTxItb+7uxsmkwkWiwWBQAB5eXno7e1l1qOVzmS1WlFdXS15fRbpA2u3IqPRKBhTeJ7H8vIy3G43urq6EIvFErwKGxmvkKUVbQ6yysEOwlbYrYjneYTDYQwMDODw4cOaLA5jY2NYWVlhptGcZ1KPOF2sHIiFJ1qpkOO80lArFJLAY4fDAbPZrKgYJCNQ0tfL3WeWEiUnJCjVK06fnJzE7Ows2trahP3VSX2pBtNqyUu3X6pucawAgd1uh81mQ21tLQKBAM6ePSvEbYyMjMDpdMLhcKhS8OSQacoMoI5CJydAj4+Pw+fzoa2tLcF6nRaqUlkZ8O7BaPjEJ4CmJsnrxVCi04ifAfF84Hn2mR/0XJDalEAqL0G6FAe73Q673Y7a2toEGlwoFILdbpe0orPKv+yyy3D//fdjaWkJDodD9SFzUnODXEePSUlJCebn52Gz2QCs0UaJokNDK51Jr9ejvr5+Q4XO9zPicfndijiOE+bm7t27EYlEMDc3h/HxcZw6dQo2m03wKrDiaNKJLK1oc5BVDnYQNttzEIvFcOrUKfA8jwsvvFDTS2N6ehper5eZplWQJv+LAykBaaVCit6ipg104HFRURHm5ubSLgiz2szKB0h7I+QoV3R+KYEJAAYHBxEKhRKs62q4qanu8JMq51wqPRwOo7e3F5WVlSh9l/ayuLgIj8eD0dFRgX7kdDqZtI+tqjiIwaJoxeNxDA4Oguf5hPMbSDqpg1WWprbffjvw3HPAd7+7FqD8Lp0uk3QeOQ8UoEzTYv3Psoyz6lFDq2OlExpceXm5ENTs8Xjg9/tx9uxZgX7ECgAG1razPHjwIN544w1ZapESBU5u7O+880587Wtfg9/vh06ng8FgwJ133rkuZkJNrASdXldXl3EhM1XQXqrtDq2HuRmNRpSXl6O8vBw8v7aNr9vtxjvvvIN4PC4cwEZ2lEsnsrsVbQ6yysEOghprTaYQDAbR2dmJioqKBE6qGng8HszMzCRVrxSFKBqNahJgpBZIqcWffBJ6TXNzs2BNS5XPn0peuYB0JYFMKa2npwe5ubnYu3dvwhiQRSad9AW1SEWAXllZQX9/P+rr6xM4rXQwKaEfnT17Fjy/dkKuy+VCbm4uDAaD4G0QQ40ArSbQNJl+qUmPxWLo6ekRDvii75147iu1TU54BgDeZgP/6U8DDz4I/Pa30F1xRUb7JhY8UxVWtAjPtIeS9TyoUXqIEl9QUACHw4GlpSXU19fD6/Wiv78fsVhM2CpVvCXl1VdfjRdffFFT3IEWHD16FI888gheeOEF8DyPD33oQ9izZ49s7BOw/j1BG2SKi4sTgt+3KqSe9e2IVA5B4zhO2MZ3z549iEQimJ2dxdjYGBYXF2G32wWvAk1RTBZZ5WBzkFUOdhA2y6qxsLCAkydPoq2tDS6XC3Nzc6o9GMvLyxgfH5dMl1tMkwk8VnONGqtXPB4X6DV04DErL0t4EnPF1QgOqQhNqVhqw+Ewzp49i/LycsG6Lm4363wFulyWsESQjngPrXkXFhYwMjKCxsZG5pkbpN25ubnIzc1FdXU1IpGIcOiV3++H3W6XPHxNbaAtK9Yik/MAWKPAnT17FqWlpcL91AJx21S1/aabgKefhu573wN/9Cg4o1GS8iZXTrIxLcnmF0PNvVHyWqh5P5DriFBttVphsVhQVVWFSCSGT5iVAAAgAElEQVSCxcVFuN1uDA0NITc3V/AqXH755bj//vuxvLwsGCu09E9NekNDA/7qr/5KU35C0xIHINtsNpSXl0vWt5Wwk5QDJVqRFhiNRlRUVAjnofh8Prjdbrz99tvgeV6IsUnWq5A9IXlzkFUOskgJExMTGB0dxaFDhwTtXi29KRgMYnh4WFGIkqL6KAn3WpUKNSBeieHhYUSjUbS3tyu+ZKUs6HLBp2riA8T50iVQ0VheXha2tmQFlot3kZEC636w2kuspiSdfNKCpJr65BSH8+fP4/z584JSpxZGoxGlpaXC7keE9jE6Ogqz2SwEk0rRPrTMA3Idi+JCC9Nahd9QKIQzZ86gvr6eyWfPGN3HYAD3uc8h/sUvCgejiSlvUmWLnwlxoC2ZW1Jtp/MlQ/chyFQAs3gcaNDvURJLZDQaUVRUhMnJSbz66qvQ6/W4+OKLMT09DY7jsHfvXrz00ku46aabEuZPpgOwtdKpjEYj6urqtg1VZycpB7FYTNVBlVrBce9t49vY2IhwOIzZ2VmMjo7C5/PB4XCgpKQERUVFqr0KWc/B5iCrHGSRFHieR09PD/x+P44ePZrwolGjHESjUQwNDTGvU+LG00KE2BoPADk5OVhZWWEKUGoWMDmlIhQKobe3Fw6HA7t27WLSMaTyaqmXFe+gJDiRQ4bEAnuyC/78/DzOnTuH1tZW5r7jdOC3Vg+OnCDIuv9KQrCYL08WclqZ4Hke586dw+rqKlpbWyUXR7Wep4KCAoGORA5f6+vrQywWE/ayz8vLWzdHtFDd1ChUdF45Sgs52K2xsTEjVmVFxeHyy4H9+4WD0SDy2ChRdcR1Sz3XYqWSPBOpKFVbKZ3nefzsZz/DD37wA0QiEXAch5deegn/+I//iObmZlx++eV44YUXUFtbK3i3yA4zcvFEqQj+WsFxHOrq6jRtF7zZ2GnKQTooP0rIyckRDgfkeR6Li4uYnZ3FyMgIOI4TvApyJzZnlYPNQVY5yEIzwuEwurq6UFhYiIMHD657qJX2oo/H4xgaGkIoFGKmJxNoSb4TIYAcuiNGslxgjuOwsrKCnp4e1NbWwuVyqW5zKhZJtRQnIkhGo1EmH5z+LskN59/bMnFychILCwtob29nLuAsYUxtn5SQzHiJ+ywWrGOxGAYGBpCTk4OWlhbZeZCMAEzoR4T2QbanXF1dFXadcTqdsv1OVYAk1A3ynQbxcLS2tgo7iInHgH5+xGWkTbj9m78BPvlJ4P/+X4CipiTtkWBArBACygoy7bEieel5lE6LuZZ0lqIcjUbxb//2b+B5XhDwwuEwfvCDH+DRRx/F9ddfj0ceeQS7du0CsHbvx8bGYDQaUVhYCJfLtW4XOTIPyDuuqKgIDQ0N69oh5blT2hSAzgsA5eXlTAV1KyOdVJzNRioxB8mC4zjBoNLY2IhQKITZ2VkMDw9jaWkJ+fn5gleBXnOyW5luDrLKwQ4DbTXNBJaXl9HV1YXGxkaUlZUxrxHzSsUYGxvD6uqqZN5ULPtylmy5RVguVgBY28FmaGhICDymF0lWm8U8aimkMxhXvABLeSPklKF4fG0HG51Oh7a2NsEaTYP22tACdSwWw2uvvYaXX34ZFosFH/7wh3Ho0CGmMpKsMpSMkBqJRNDd3Y2ioiLhMD6WVV5tnICYziJuu9FoRElJCUpKShCPx7G0tASv14uxsTGYzWaBH04LaJm0PE9PT2Nubm7dwW6k/eKYBzHo+yw1p1Xfs71717wG/+//ATffDJSWZtRjoUbhoJViVl5x+UpzQm29asB6j6ysrCAcDkOv12N1dRV6vR4mkwlTU1N47LHHYLVacdFFF+G3v/0tPvKRj6CgoAA8zyMYDGJ+fh4DAwMIh8MoKCgQYmZ4nscrr7yCb37zmzAYDMJZLd/+9rdhMpkUaZpS84M1Hg6HI6lYl83GTvIcbAVFx2QyoaqqClVVVeB5HgsLC5idncXQ0BAeeugh7N69G3/0R3+EYDCo2cN07Ngx3Hfffejt7cXbb7+NgwcPMq978cUX8bnPfQ6xWAx/+Zd/iXvvvTcdXdsR2BkzPQsBmTzr4Pz58+jq6sL+/fslFQNAnlY0NTWFhYUFZpoai7Ea2g7Lc5EM5YcsiFNTU4LVNTc3N8FST+clbnua3kNTPdTWq6a/rLGi+6iUl5UWjUZx5swZ5OXlCZQpYjWl/+ixocv7+c9/jn/913/Fm2++iZmZGfzLv/wL3nzzzQQFY6M9CoFAAKdOnUJFRQUqKys1ly22PtN/Yss6KYe+93q9HoWFhdi1axcuvPBCNDQ0IBaLoa+vD8ePH8fY2BiWlpZU70mvJZ3neYyOjmJxcRGtra1JUTho6zlrLpDfWIq1+FkQPu+6C4jHgUceSYtSJDXPV1dXMTMzI7sTjlx+qXSxN0E8HlLzgswJ+o+cjC0F1nvD4XCgqKgIkUgEJpMJ4XAY0WgUBw4cQEdHB37961+jubkZL774YkL7zWYzKisr0d7ejn379sHhcGB+fh6dnZ3o7OzEN77xDUSjUYTDYcRiMbzzzjv45S9/qcrrITU/gMRtM3NyclBbWytZ3laG1u0/tzI2w3MgB47jUFhYiKamJlx22WV4+OGHUV5ejq9//esYHx/HZz7zGfz85z/H0tKSqvJaW1vxzDPP4LLLLpO8JhaL4a677sILL7yAnp4e/OQnP0FPT0+6urTtsTNmehYCMnHWAc/zGBgYwMjICI4ePQq73Z5UG+bm5nD+/Hnhf7EgJSdQa6HtiIVfrUI2AbGikwOixMGr4rxkceS497YUZQmSAAShgCUwkPiBZPj6xLqlVQAPBAI4efIkKisrUVFRIWkhZo0l8RS98MILKC0tFdqel5eH559/Xui/WJFiCUx0mpo+020Q99nn86G7uxuNjY0oKSlJ2pqrVilhCdG0YsHzvLDjzL59+9DR0YHc3FxMT0+jq6sLg4OD8Hg8iMViCdbpZDwp8Xgc/f39iMfjaG5ulhQElITjZEHGIRaLCTtZCYpEWRnwp38K7te/Bt/TIzkXSJvl5qLUffH5fOjr68OePXuYu1Ep5U9nupLgLAY9FuJ3BEn7yle+ArPZDKPRiHg8joKCAnz2s5/F//zP/2BwcBBPP/00fv/73+PXv/41s20GgwFFRUXYtWsXDhw4gJWVFeH5CwaDiMfjCIVC+M1vfiPZP0C9Z4bc44aGhowEwm4EdpLnYKsrOjU1Nfj85z+Pl156CdXV1fjzP/9zdHV14eqrr8aVV16JBx98EN3d3ZL5m5ub0djYKFvH22+/jV27dqG+vh45OTm45ZZb8Nxzz6W7K9sWW3d2ZJEU0q0cRKNRdHV1IRQK4fDhw6qCmFhtWFpawsTERMJv9KIpXjxpCxzttmYJk3L1J0thIVQUk8mEpqamdcKVXF6yEMoJDqw+kz+OSzy4Ta0SRcZJq6V1cXFREKLlePFyYxmJRBCJRKDX61FdXY1oNAqDwQC/3y/0QaxI0f2nx4RFYRDfe9oazboXc3NzGBoaQmtrKxwOR9K0lEzQnAj0ej1KSkrQ1NSEAwcOoKioCIuLizhx4gROnz6N6elpBIPBBPqP2CtB6qDHgWxVmpeXJ3vqbCpWeSDFOIHbbgMcDvDf/S54ieefVipYbSNtEM8Lj8eD4eFhtLa2SioGyXih0pmuFGcgVjDF78W2tjY888wz+Id/+AdceumluPbaa9Hf348XXngBZrMZoVAIRqMRDz74oKS1lfb81dTUJLxjyTkxOTk56Ovrw/z8/LozVJRok/T7iOM4VFVVbevA0p2mHGwlz4EcOI7DxRdfjG9+85v4/e9/j//4j/+Ay+XCo48+mlK5U1NTqKqqEv6vrKzE1NRUqs3dMdieKnwWktDr9bIHYWmB3+9HZ2cnampqUFNTo6kN9MIXCAQwMjKimdbDSmMJjSxLNmkHsbyJudVkwWJhdXUVfX19qKmpWRd4rAZ6vV4QlFnQSnGiebtqxkpsdZb6BNaoYtPT08KORMncIyJE7N+/H8ePH0dxcTF4nsf8/Dyuv/76jAnY4r6Q36ampuD1erFv3z6BSkPmhPj+bzTNSSqd47iEw9cCgYCw+1E0GhXiFOx2u6xXIRwOo7u7G5WVlSguLpYVZjKl9KhJ5+x28HfcATzwAPDb3wIy7n8WaAWS7sf58+cxMzOD9vb2BAu1kjeKLkPpvqYjXUmpIqcim0wmyXtotVpxySWXwGq14oEHHsDs7Czi8TjMZjNWVlbgcrkQi8Vw+vRpXHLJJQn1i8eioaEBF154obA3fSwWg81mw+c+9znYbDZ4PB6cO3cOBoMBTqeTGdRMg77/8Xgc+fn5KCoqku3zVsdOUg7i8c2POUgWZWVluP322/Hkk0+itbV1Xfq3vvUt3HDDDYrlSHnfs1hDVjnYYUiX58Dj8eD06dPo6Ohg7ocuB51Oh0gkAmDNoiy1ZSm5Vi1dSG1ekk9cJ/0yoBUYerH0eDwYGRlBU1PTusBjtW0WX6+mzXS7paDW0ituM0up4Pm1bT1XVlawb98+QZCiX450H+TqJScFf+pTnxKEU47jcPToUXz0ox9dd31/fz+efPJJTE9PY//+/fjEJz7BPENBTZ9pxONru2DF43G0trYqUrNoZUrcb9r7k4yFPNV7mZubC4vFgoqKCkSjUSwsLGBmZgaDg4PIy8uDy+VCfn5+ggC8urqK3t5eNDQ0oLCwUNKLxOoPS+EQe2VoT15aFIcbbwSefhp4+GHg6FHg3b4kUz7P85iYmIDP50NHR8c6IY5+LtQoq6w4A6lnI904fvw4vvzlLyMSiUCn06G8vByPPPKIYHUX97+jowOLi4vIyckBx3GCQkH6LH5/S83Nb3/723j++efxxhtvoKurC9/+9rcFyyrZsjcYDMLr9WJ4eBihUAj5+fnCSc60N4cu32w2y8aobRfsJOVgq9OKCCKRiCQN7ZVXXkmp7MrKygQ2w+Tk5LY5kG8jkFUOdhjSEZA8NjaGiYkJHD58mLm/vRKIgkKEtXA4zLwuFautEl1DS4AnWUQnJycxPz+PtrY25OTkyApWrBerkvCUqf6SdgFsIV68WMdiMfT39wvbeiptPSsuixaS6O8OhwN/+7d/i6WlJej1euTm5q5r98TEBL761a8CWNut4tVXX0V/fz8eeughVacMS6VHo1H09vbCZrOhpqZG0QJEj4kUjUmKDy7+JIKjWkVCq+JA+OFFRUXgeR4rKyuYm5vDuXPnhO0pc3JyMD4+jqamJtjtds3zTOx9YSnF4v7S48DqoxQdSGibwQDcfTdAHYyWrGJADiVsa2uT7acaxUDq3cFSsuXGgdSl1rAArD2b9913H8LhMJaWluB0OjE2NoannnoKn/rUp5j59Xo9rrzyShiNRpjNZgQCAeh0a2eyNDU1obm5WVX9RqMRN998M/4/e28eH1dV94+/Z81MkplJJpkl+9I2W5M0pS0tBSqbxZYClk2tIH4f0aKiAirP73n0yxcFhUcFd+mD+LC9WFwesdWCSIuoBWya0qbNvu/JJDOTdTL7vb8/0nO4c3PvzJ0lTRPn/XrlNUnOnHPPOXf7LO/P53PzzTfj+9//Ps6cOYOLL76Yrh1YuGdJZe1gMIipqSnY7XZ0d3fTQoDcAldyuRx5eXno7e0VXfNKwWpTDlaC58Dtdi9ZGtMtW7ags7MTvb29yMvLwyuvvIKXXnppSY61ErE6rvQkKOLxHDAMgzNnzsDhcGD79u0xKQZkDoFAAD09PZifnxeMFeBamYQQLfWG3x6Np4JhGHR0dGBubg61tbWicRVca5xQrAAQmtObyxEX4ofzhexwvHcpHoNwAgqBz+fD2bNnkZGRgbVr10ZUDPhj8vnPpJ4Elxuu1+uRmpoqGFD5zW9+E9PT00hNTcX8/DyMRiPGxsbQ0dER9ZpJu8fjwZkzZ2A2m1FcXCwahyC2J+HG5oOrCPA54dx2rpWaHycS7vqPtG6FQgGdTofS0lJs2rQJZWVlmJubo/s3MTGBycnJsPdOvFZvblyI0D4IxQmQ9ZPrge7HFVdAdq4wmmx+PmrFgGEYtLW1QS6XhwjBYv0TTaXi7gOZD3cv+IoBl9cvFEPT398Pn88HjUZDn6MymQzvvvtu2Pnt2rULBoMBBw4cwK5du1BeXo5Pf/rT+P73vx+iwERSGsl8r7nmmoiWWYVCgaysLKxbtw6bNm1CSUkJgsEgmpqa0NDQgJ6eHuj1eqjV6lUhVK9kKg4fK2UtLpcrpjiVV199Ffn5+Xjvvfdw3XXX4dprrwWwkNZ59+7dABaMLj/72c9w7bXXorKyErfddhvWr1+f0PmvZCQ9B6sMsSoHXq8XDQ0NsFgsWLNmTVzcO4VCgZGREerO5lvPIgluYtY4/otYrH80SoXf70dLSwsyMzNpUJ7UvmLHJS9hqbQccs6i4UULzSvSHOfm5tDW1obS0lIYjca46CHceYlZM7kCM4HJZEJ3dzdycnLQ399PCyF5vV5Rr0Q4WgtZ09q1ayk16UKJIyBz5s6fPz7/vuAqNnwai9C1b7fbabIAuVwOh8MRQj8i1XGVSmVCgmhjVSy4e7Doer73Xsg+9SmwzzwD9gtfEFWcuHvCsguB1y0tLTAajTRXeri5L3UcQTTtQsoTwzAwGo30WUCoOn6/n6bh5QrZ3H2srq5GTU0NWJbF1772NdF5hAP3/BKqUl9fH4rPpR6N9DzQ6XRIS0tDfn4+VWomJyfR3d1NY4HMZvOKqorMxWrzHKyEtcRaHXnv3r2ClNbc3NyQDF67d++mykISoUgqB6sMsQQkT09P49SpU6isrITFYol7Dna7HXa7XTBWIZKAEe4lKyQ4k08xay1fYOeCcLSLi4thNpsTFgvADzSVSmMQo7eIBU5xLbHABwHY3P0gfZ1OJ3p6elBZWYm0tLS4hWD+XPhUC7G++/btw9tvv029B2NjYzCZTKioqKDzlaLgsSyLV155BW+88Qays7Nx2223Ydu2bQDCF3m7kBQHIYQTIPno6emBz+cL4dibzWZafG12dhYTExMYGBig9KOsrCxBj+CSByCHuw+qqoBdu4AXX4Ts5pvBniuQtcig0N8PPPUUcM898BmNaG5uRm5uLiwWi6hBQeq5jrTXSxljwEVGRgb27NlD6wswDAOVSoVPfepTkvZfyMBAEM19IZfLcdVVV+HIkSO46667oj7/BoMB5eXlVEHo6OjA7Owsuru7aZYui8WC9PT0uAxR5xMrhYojFSth32NVDpKIH0nlYJUhWs/ByMgIOjo6sGnTpoSUs5+amoLNZotJAItWcONazvh9uZZ7vhIBfCAsV1VVIT09PeaXv9CcpVpY47XUCgVck3Vz+w4PD2NiYoJm7xFSHqLhRYvxrqXMWaVSITU1laaM83g8eOKJJ2jmk0jHJmP/6Ec/wptvvgmdToeBgQE8+uij+NrXvoZLL710UR9unAif9sW36oebezyW6UQK1yRmRKPR0FzeQudSp9NBp9NBJpPB4/HQFJ/c6rgGgyEumlXC2r/4ReDIEeAXvwC+/W3h/nI58Oc/w5+fjzObNwt6wMQUabI/XGupkGcCWJzJTIpBI5H796UvfQm1tbV46623oNfrsW3bNpSWlkrqL2RgEDs+WSPfyEBwzTXX4Hvf+x4++9nPRuUVUSqVISl0WZaFRqNBRUUFKioq4PF4YLPZ0NraCpfLhaysLFgsFmRnZ1/QwjdR1JI4f3C5XEsWc5BEeCSVg1UGhUIhGgDMBcuyaG9vx9TUFC699NKEPPRcLhd6e3tFOf/hXpLxCMpSlArui394eBh2ux3V1dXQaDSCwj33k/t7OIWEP59IbvhEUHr4fbjzYtmFQE2/34+ampqQaqyRvDPhXM78vhqNBh0dHfD5fMjOzqYCKR9+vx8//vGPkZeXh8HBQVRXV+P999/HyZMnUVFRIekaYJiF4l5vvfUWjEYj/H4/VXh+85vfCCoH/HMVSSHiW1/5dBap3h3+vMUQjfBIahiYTCbk5eVJOj6wEEiam5uL3NxcBAIBTE1NYXR0FO3t7ZR+ZDQaQ7JWcdcsplAlTHGwWoFPfhJ49lngE58AzsUPhPTPz0dgwwYEDx5E+b590On1UR2fv09iCiH33IsplNzPeJU+frtcLseVV16JK6+8ErOzsyGFIxMxPgGZv5gxacOGDZicnERfXx9NZS1Ee+Meg2VZFBcXh8Rt8RUPjUZD02MzDAOHw0GVBa1WS70Ksca8LRVWE61opSDpOVg+JJWDVQYpngO/349Tp04hLS0NW7duTYh70efzoaenBwCogEEepJFeovEKylL7MswHqS5rampoCk4+wlGRhI7LFyb5+dWjFSZjpb6QOTAMg0AggLa2NqSnp4fEkEixzEejhMlkMmRmZmLz5s1wOp00uFin01G+O7EGDgwMwOfzwWQyYXBwED6fD0ajEa+99hruuOOOiOfR7/ejvb2dFlhTKpVwOBxgGAZZWVlwuVyi+xJrnIDYurljiwW6knESpTh4PB40NzeH1N+IRThXKpXIzs6mY8zMzMDpdGJoaAhyuRzZ2dkwGo1ITU0N62ESEhKF1h+OGhcyt09/eiFr0Y9+BBw4ADkvWH5qagqTGzeipLERmu5uyDdtWnqPhohCKaQYCRkThK4P7vNFyrUh9nyOdO3EC5IF6ciRI/jMZz4DYLGHim8IysnJgcFgCBkn3BrkcjnNxAUsxBDZbDacOnUKfr8fJpMJVqsVmZmZy06DSSoH5x9J5WD5kFQOVhkiKQculwsNDQ1Ys2YNDXKLF8FgEJ2dndRjIZPJEAgE6ItL7CXK/RR6+Qr15SIaIZsEHhuNRuTn54sKdEJ9I0FIACSpXIXmLMYLjtcSSdo8Hg9aWlqQl5cXEkMSj3dGbF7k+wqFggqcLMtiZmYGDocDfX19UKvVMJlM0Gq1lEddWVmJlJQU6HQ6DA4O0gA5MY8IWZPZbEZubi4qKyvR2toKg8GAnp4eaLXamALLEmH5DXe/8eNeuP/jepiEKC3cuZHA63Xr1lHhK1HCr16vh16vR3FxcUgee7/fD4PBgKysLOjPWen5EBJ6hdbO/Q434DjkPtDrwX7uc2C/9z3I/v53MB/6EG2amJjA4OAg1t9+O/Cb30B28CCYjRtF1xbpvC5Fu9BaI0HIEs/tH0+sQyKuj09+8pOSvb06nU4wT7wQZUkM6enp1KDh9/tpyt7Gxkbo9XpYLBaYzWbRjHJLCYZZGRl+VhPm5+eTtKJlQlI5WGUIV+dgYmICTU1N2Lhxo2jRqWhBqCsej4f+j/viFHoB8Xne4V4+5DvhhGmhFygJzJbL5SGBx1IqHsdLcYrV08FvE1OiuMKkkFLS1NQUIkRKWVOilDDyfYPBAIPBgNLSUng8HhqkXl5ejsbGRpqP3WAwgGVZnDx5Eps3b160drlcjrm5ObS2tqKkpARZWVlgWRZf/epX8eijj6Knp4dynG+55Zao5n6+ufb8c0aoX3xrPP9zcnISPT09qK6upla0SIprrHQTjUaD3Nxc5Ofnw+fzYWpqCuPj4+jq6kJqaiqlH6WkpMS0NxHpODfdBLzyykJhtEsvhUylojTAuro6KBQKyD78YeCNN4B//3cgNTUuAXq5EM4gAnzw7OMri9xPrtAdjVFFSjs5P4S6JtZOoFKpROMiYrW4q1QqSoVjWRbT09Ow2Ww4fvw4ZDIZzGYzrFarKI0x0VgtnoOVdL/Emso0ifiRVA5WGYQ8ByzLore3FyMjI7jkkkvClr2PFv39/ZidnRWcQyKs4ARSqTnEjU8e4lNTUzTwOC0tLSJPOhEUp3AxAdHQAMK574WOPTExAb/fjw0bNoQ8UIkQGq5vtPSEiYkJmEwmSful0WiQn5+P/Px8VFVV4ejRo/jnP/+J1NRUXHHFFWhsbMShQ4dClAMiQDqdTnR2dqKiogLp6en0WFlZWXj88ccxMTGBP//5z2hubkbqOUExnEdKKhIZJxBLO7AwZ5vNhpGREaxfv36RQM6lvHCt8dxjkHbup9S5celHLLtQfM3hcKCpqQkymYwqCnzLXlxrVyohv+8+MPfdB/b3v0ffxRfD5XJh/fr1HxgLbrgBzMGDwJtvAjfcENKdS+Phxwdw92c5z63UdoZhMDo6iqysLADCdEexZyD3XHMhxTspNq4YZDIZSktLRSvZhqMVRXOMjIwMZGRkoLy8HF6vFzabDe3t7Zibm4PRaKRBzWLziBcrJf1nJKykrEtJWtHyIakcrDLwlYNgMIgzZ84AAC655JKEPhRGR0fhcDgW/Z/rKhfDUgnoAGhhrsHBQUxOTqK6uhpqtXqRYiDmkeDzrKUeN9z3loLSw23v7+/H1NQUNBrNoiBr/thc4ZlPaZAiSE5NTeHWW2/Fa6+9FvbBLdRXrVZj165d2LVrFwBgcnISCoUCv/71r9HY2AiLxUIr/tpsNgwNDdHAcaH9ys7OxvXXX49f/vKXmJ6ehk6ni6hM8QVILqRSQZZaOAwGgxgcHMT09DSNj+EeX4j7T+Yf6VriHoeA66ETs/jrdDoYDAYwDAOv1wun04ne3l54PB5kZGTQGJN46DpyuRzMZZeBvegiBJ98EoGyMlRt2BDiSWJqa4HCQuDQIUHlQMg4InZ8Me8c937g/n2+FANS8TszMxPWc6ldhebPB//cS1X6heIlCCI9E/Ly8pCeni46djS0IqlISUlBYWEhCgsLwTAMnE4nbDYb2trakJKSAovFAqvVmlDBcrV4DlYSPWp+fl6Stz+JxCOpHKwycJUDj8eDhoYG5ObmoqSkJKGuVxJ8yhcwpAhXsQbcSu1LePek4jGZY6TAUzGhivtyE3s5cMfij7OUlB4AaG1thVwup9l/IvWXKjyI0bqMRiM2btyIt956C9dff72o9VLKmkkw8+HDhxEIBOB0OtHU1ASfzwe5XI6KigqkpKQs6s89psFgwMUXX4wjR45g74dbhjQAACAASURBVN69cccJ8BVI7id3jEhxApHGFmsPBoPo6upCMBikFnOp/aVcL6S/EN1PqD9/D+RyObRaLfLy8pCbm4tgMIjJyUlMTEygq6sLaWlptKYCNwtapLmRvQsyDHpvuAFrH3oIa44dg6yuLnTtMtmCUvCznwEDAwuKgoS9iURxFFMouesWozmS+z8eDx1p9/v9aG5uhtVqDVEMEgGxPYrWq0TWn5GREbE2TiI8B+Egl8tDAuxdLhdsNhsaGxvh9XphMpmo0SEe4X61KAcryXOQpBUtH5LKwSoD4dpPTk7i9OnTqK6uppkgEoW5uTn09fVFtE4KCVZCrn5+33B8/kgvV5/Ph+bmZiiVSpSUlIgqBtEeN9yLnx9Iyw005cYJANFlwokEktYyOzsbeXl5i17AkcaOxrPD/+6NN96IF198EXv27An5v5hluq+vD++99x5SUlJw+eWXU6oEAfEMpKamwuv1IhgMwmAwYGBgIMQybTAYQlKyEuzZswcvvPACbrrppiWNExDqL7TvQggGg5RuJ3Zsv9+P1tZWpKenY+3atYvunaW0WodTjoV+546blZVF6UculwsOhwPNzc2UfpSVlRWS/Ujs2OSaNl90EbBrF2QvvQTccgtkOTmhc7/uOuDnPwf++Efgi1+ULHjH2g5ELlAnRF8Kp1QKjeH1etHc3IzCwsJFFtPlpjvx6UwpKSk0xWk4nG+hOi0tDaWlpSgtLUUgEIDdbsfw8DDOnj0LnU5Hg5qFjA7hsJqUg5WyjiStaPmQVA5WGRQKBebn53HmzBlcfPHFCY/093q96O7ujijAc4VgIa4sH1xrnJhbO5JgNTs7SwNXx8fHQ6y/S2W5D0chChd/QL4XzhIZrq/b7UZzczOKRYKsl5rGdOmll+Khhx7CSy+9hNLSUmzcuBEpKSkh8ybjHzt2DD/60Y8QCAQgk8nw61//Go888ghNsUrWHggE0NLSgoyMDOTn50MmkyEnJwfBYBBTU1OYmJigmYmIwEnoNtu3b8fDDz+MoaEhyUGU0e6Z1HapSiSf3kUEQ4vFgpycHADS014ut+DIbU9LS0NaWhoKCwsp/ainpwdutxsZGRkwGo3IyMigyjPpT65pkqqV/eIXwb755oIS8MgjoQc0mYDt24E//Qm4+25giXjmBNHuf7RxHh6PB36/H52dnVizZg0yMzNpG3mOJEqwj6Vd6HilpaWSLNBC9L3zBaVSST0wLMvSuhEnTpwAy7K0ojgpBhgOq0U5WGm0oqRysDxIKgerCCzLorW1FT6fD1deeWXCA7MCgQA6OzsRCAQE2+MRsiMpDvxAU+4nANjtdvT19aGqqgqpqamw2+0RBexIc44Esb5kLdEI4FLiG8h6p6en0dXVhcrKSlrV+nzRmEjf119/HUqlEs888wzNGvKtb30Ler0+ZOxgMIinnnoKarWaVqJ2uVx4/vnn8a1vfYsqER6PB42NjXjttdfw4IMPhqyJpEk1mUwhgbFnz56FQqGgisJHPvIRvPfee4JZiyLhfCkOXHAFSI/Hg6amppCMTNy5iSnOpP+FohjwkZKSgry8PKrkTU9Pw+FwhCh52dnZ8Pl8aGlpwdq1a5GRkbEwntUK3H475M8+C2bfPsiqqgBw9uDGG4EHHoDs+HEwl14qeu0ulUclEeOPjY3hoYceQnNzMxQKBT760Y+irq4u5Pv8/mLxEWLeSfK/eMCfQ0FBgWSh7UIRRmUyGU3bW1ZWBp/Ph/HxcXR3d2NmZgaZmZmwWCwwmUyC787VohysJFpRMpXp8iGpHKwS+P1+nDx5EhkZGUhNTU24YsCyCylLvV6vYLvQC0yqxShaAZ0ffDk4OEgrHpP81/yAU26AIff3pbCuc1/S0Y5L+ovxgkdHRzE2NoaqqirR6s58DrzQOFK46ULzZhgGU1NT+M1vfoPc3Fx0dXUhMzMTw8PDOHr0KG688caQPvPz85ibm4Ner8fIyAjUajUyMjLQ19dHvzM7O4v29nZUVlbipz/9KU6cOIFt27YJHhsItUx7PB44HA50dXXh8ssvh8lkwszMjGhefu4ehPtb7NhCiFf4JKl2y8vLqbLHB5fOITQ/ob+JUsGntXE/z6dSpFAoYDQaYTQaqZJI6I9utxs5OTlQKpWhAu+//RuYc4XR2AMHAO51e9llkOt0CB46tOBFEDk+95MgmribpbLYsyyLBx54gD5XdTodDh06hKKiIuzdu1e0vxAtKdLzhP8s5j4Dor0GiEInFcvpOQgHtVpNs6ixLEuDmjs6OqBSqWilZhJsfaEoOfFiJdGKkjEHy4ekcrAKMDs7i5MnT6KsrAy5ubkYGxtL+DH6+vrgcrlCBGsCoZcLCYxWKpVhX6Dxvnzb2trAsmxI4DF3TkJCVbjASzGrHNcaF0mwDldrIhLCKQYkMww/ew1/DVwLlxSPQjiPDFcQIb+PjY1RK5xSqYTL5YJGo0FbW9si5SAtLQ1ZWVnUMjc0NAS1Wo2tW7cC+MDjQzIS1dXV4bHHHkNVVRWuuuoqXHXVVVDwKuVyodFoUFBQgLy8PNjtdszMzGBkZATt7e3Q6XS02q/Yy1CI0iW0djHEK1xPTk6iu7sb69evh1arjbq/0LXIV54jzZ/7yR8nUnxQrIKxTLaQ/YgUTqyrq4PL5UJ/fz+tf5GdnQ29Xg/F/v3Af/0X8I9/ADt2fDBGSgqY3buB//1fYHoa4FXmlTI/sRgBvvAcy/rJOGIYHh7G4OAglEolfD4fNVYcPHiQKgeREM3zU+g6ETPq8O8X8jfJEhQNVoLFnRsbAyzQNm02G5qbm+F2u5GdnS1qGFtpWGmeg6RysDxIKgcrHDabDa2trbjoooug1+uX5BjDw8NwOp2CbcQqJfQyYVk2bMXmeAQrktFDLBg3nIAu9rInwpBY1hJuX7E4AYJYlCGx/QgGg2hra0NqaioqKytFhVmZTBYSDC1lbDJvqUKoTCajRYkCgQBqamoAAA6HAxUVFYv2Vi6X47777sO3v/1tBAIBBINBqNVq3HnnnRgeHsbExAQ2btwIhUKBEydO4N1338Xw8DC0Wi0OHDiAsbEx3HHHHWHnZbfb8cgjj6CtrQ0ymQyXXHIJvva1r1G+e19fH1JSUmhefm5aVCkCJP9vMUs9n84RaeyxsTGMjY1hw4YNIVl9uHt3PgNMhdqFFGihT+4YUj1SY2NjGBkZQW1tLdRqNXQ6HaxWKxiGofSj7u5uaMvKUJ6XB/mPfgT59u00voBl2YWsRb/+9UJRtNtuCxk/Gs+Y2NzDeWrEFEupFv3Z2VkEg0GoVCqkpqbS5w65Ps/n+efPV6ifQqHAmjVrohb0hd4PFzq0Wi2Ki4tRXFyMYDAIu92OwcFBHDt2DGlpadSrkMiaQecLK8kDkqQVLR+SysEKBcuy6OrqwsTEBC655JKoMy9Ihd1uD+uJIAKREGeeZdkQIVtIoOB7IqQE8M3NzaG9vR3FxcWLst6QvoD0HN/8vlKEZKE1i1ka+UIE90UpNA4XXq8XLS0tyMnJCZvWMJyFMJGcaZZlodfr8fGPfxwvv/wydVHn5+fj6quvFlx3dXU1nnrqKZw+fRpHjx6FSqWCy+WCz+fDBk4O+9/97nfQarXQ6/Xw+XwwGAw4fPgwbr31VtHrm2VZfO9730NLSwstcnfs2DFMT0/D5XKBYRjs3r0bV199NSYnJ9HW1gaGYWA0GpGdnY20tDRRZUssTkCqB4m7B/wxent74XK5UFNTI/iivpACjPlzB6Qr9mKeuMHBQTgcDkEvmFwuh9FoRGZmJliWxfz8PCbvuAOmxx7D4E9+guBNN8FkMi1kPyovB8rKFmoecJQDKR6TWO8JKco0t13ouTc6Ogq/34+6ujo0NjbS/VQoFPjEJz5x3gOMxcbg7lFRUVFM7xnudbASoVAoYLFYoNVq8aEPfQhzc3Ow2Ww4efIkgsEgDWrOyMhYEetcSZ6DJK1o+ZBUDlYggsEgTp8+DZVKhW3btolaieO11szOzmJgYEC0PdwLVqlUwu/30xgAQDrdQSxeAFiwUPf29qKiokLQokBeqmJUlFgs91L6ctfHHycaXi9XmJybm0NbWxtKS0spT1toz7jz4mfEiYRY17xnzx7U1NSgvb0dBoMBGzduDDnXBKSvXq/Hjh07UFpaittvvx233XYbqqqqQvZsenoaKpUKJpMJbrebpuX1+/3QaDSCSo/b7cbp06eRlpYGl8tF+/z973+nGY9++ctfYnZ2Fp/85CeRn59PU/0ODAxgfn4eer0eWVlZyMjIoC/NRAax8j1KnZ2dkMvlqKqqCmuJvxDiBOJt58+dYRj09fXB4/Ggurp6ERVQyHCg0+mQfsstYP/yF+QfPgz73r3o7++n5y736quR/uSTQGcnsG7dBbV+oT0gxe3Wr1+P7373u/jFL36Bt99+G+np6fi3f/s3XHnllXQcLoQofrEi2jWYzeaQDErRYCV6DsRA6HA6nQ5r166F3+/H+Pg4ent7MT09DYPBAKvVCpPJJOgNvBCwkmIO/H7/BbuPqx1J5WCFwe12o6GhAYWFhaI5pgmlJp4HgNvtlpSyVAhCcQnR9BWz1hJ6EzfwmHs8GsQol9Nc+GQ8LuVG7LjxWNe5/YV4vNEIUyzLUiWoqqoKaWlporECRAki55oIt1zusBSFJpY1l5SUSMpzTuDz+TAxMYGSkhIMDg6irKwsZB6XXXYZ/vCHPyAjIwM6nQ7T09NYu3YtzXLEXTf5VKlUUCqVYJiFFKIzMzPwer1QKBRUUUpLS8Orr76Kffv20T4mkwkmkymEwtLb2wuNRgOTyYTMzExBZUfKvoi1c6ve8qlw0cQJkLVHipUQ67dcgjNRjJRKJaWg8ecddn733QflHXfA9NprMN9zD1iWxdTUFOybNyNdoYDzmWfg/8pXaIXtSIp0LOuLx2LPsix6enrg8/lQVVUFuVyO9PR0PPDAA3jggQdCvifV6yFGcwtHbYp2D9LT05Gfny/6/UhY6Z6DcFCpVMjLy0NeXh69Hm02G7q6uqjHgQQ1Xyh7sJJoRUksH5LKwQqC0+lEY2MjamtrBek0BITnH6vGHQgE0NPTQ/PS8yFFyBbj7ccioDMMg46ODigUikXWRkCY4yuTLVTBJQKHkGWe650QGkvKnIXa+S/vaAXwoaEh2O121NbW0toBYuCnlSVULr5iEIkfLWSVT6SQSDLyEM/B9PT0oj633HILhoaGaJXn/Px83HvvvYu+R+ZGYlr27NmDgwcPQqVSwe12U1qK2+3G7Ows8vLy4PP56HXApYYpFApkZmaGUFi4BbxIpV9SwCtW4ZLUMCgoKAhblDBWj4RQO/mb+7tQf6keiXjaA4EA2traYDAYUFBQENv4VVUI7toFvPgi2JtvBqxWZGRkICMjA7jiChj/+U8M3nUXmkdHKXUsKysLOp0u5Prn0/rIpxQqTqwWe5Zl6TNMSDEiiDYAna9IhIuXIu1ClnzuPnCPT4pJxiPYJsKLvRIgk8nos6SiogIej4fGBM7Pz8NoNMJqtSIrK2tZhfN4ZIPzjQtFofpXRFI5WCHo7+9Hf38/tm3bJpjVhItwQcCRQKx7Ho9nEV+YK1jxBQ2+dUjoJRfpxScEkv/cZDIhNzdX9GEhJBQJWfL5L9Nw1nUpAoVQ33DZdbjg92UYBt3d3QgGg6ipqYFKpYpakeIGJPOpDXwhItzYYlx57lylrmtqagpdXV2oqKhAeno6rrnmGsG5azQa/Md//AccDge8Xi+sVuuiOQjN+7Of/SxMJhNef/11+Hw+GI1GzM3NIT09HWNjY5iensbll19Ovx8u2JxQBoqLi+Hz+eBwOCiFJSMjg2bQERJ2xIRLohiRHP5S9y0R7fx9jiR4cj+FEItwTJIH5OTkwGKxRN0/BF/8InD06EJhtIcf/uD/118P2dGjKOjrQ8FVV8Hv98PpdGJoaAgul4tSxwwGQ9hMX0K/c/9HlFIhiJ0fklBAp9OhoKAgZsUgXq8GED4lLhmD+3wvLS0V9aBJxWqiFUUDjUaDoqIiFBUVIRgMwuFwwGazoaWlBVqtlnoVIr3PE42VRCuKlz6XROxIKgcXOBiGQVNTE3w+H7Zv3y6pfkE8ykFvby/m5+dD/idmVeIL49xYAZKvnMubDkeZEHrx8Tn3YhBTREhF5VhfuOEstKSvUGwEsQoRepfQmvnzIpQTvV6PwsJCyQqG0JzitfoD4kKkkBImJkgBH2SkqampQUpKiqRji51rsXUpFArcfPPNuPXWW/Huu+/iJz/5CS655BLU19fTQltf/OIXoxa+lEolfYGTAl7j4+Po7OxEeno6TX3ItcJxvVIsy2J6ehqdnZ20OJ/UYy9nu9T7U4zSQsZgWZZWPeZX/eUjkoeNtlutwL59wLPPLnxWVi7Mb/t2MNnZC4HJV10VkqeeYRjMzs7Cbrejt7dXMHOVWJwAd/1Cz1QhAwp3jEAgQLOq5ebmhl1fvIJ/JETjxWRZFjk5OaJ1N6SCZRfqWawUYXSpoFAoYDabYTabAYAGNZ86dQp+vx8mkwlWqxWZmZlLbi1fSQHJSSwfksrBBQyfz4eGhgaYTCbU1NRIfmiQoMxoMTg4iKmpKcG2aOkxhNZDPApiFAjuJ/cFMj4+HlLxWOpxuf+PZHWI1oXPbwtnpWUYRvAccNdMxvd6vWhqakJBQQHMZnNcwr0UWkG8igMXXI8En7LS39+Pubk51NbWQqFQ0DgQIS8M6R+rAET6btmyBZOTk/j4xz+Or3zlKzhx4gR+9atfwWAwxLVulUoVUsCLVGkeGhqCXC6HyWSC0WgMsQLa7Xb09/ejpqYGGo1G9P5lGCYuwXC5FAty7sXaiXJfXl5O0yzHEiexaPxPfxo4VxgNBw5ArlDg93/4A34xN4fpY8dQ93/+Dx585BHk5eUBWFDyDAYDDOfqIMzPz8PpdNLMVVlZWcjMzKT0o2j2h09H4q6D7zER8sxMTEzgd7/7Hfbv3y8p1kTyHsXZrtfrkZOTE9NcCFiWxalTp6DX6+neJ7GA9PR0pKenY82aNfD7/ZiYmEB/fz8aGxuh1+thsVhgNpvj9toIYaXEHPATmiRxfpFUDi5QeL1evPfee6ioqAibwlIIsXgOxsfHMT4+HlUfAjFqTaQ5CAkWLMtiaGgIDocDGzZsgFqtpjQZfqxAuMA9Mm60FAAp7ZFe4uHWzhcmiGV53bp19AVK5k2E6HCW+WhiBeIVMiMpS1yKWUdHB5RKJdavX0+9SlKVFiEhKlKQJYFCocDu3btx+PBhfPnLX8aOHTug0WioByeWdQspvnz60cTEBLq6uuD1emE0GsEwDObm5mgNg3DXaiRvjJAHjvvdC1GxIFQyUtxNzAsn5pEgn3yLPMuygE4H9lxhNPk//oF3VCo8/vjj8J4rqHa6qQn79+/HwYMHabA6F6mpqUhNTaWZq5xOJ4aHh+FyuaDT6WjmKqVSGXMcgsfjQXNzM4qKiuB2u3H33XejqakJFosF999/Py699FIAC0Liyy+/jJtvvjmk6rDYPcA9nhBtUgjR0pHUajVKSkrCrjkSGIbByZMnodfrUVZWtuK540LxaYmCSqVCbm4urR8zPT0Nm82G48ePQyaTwWw2w2q1iiqv0WKl0IqSaUyXF0nl4AIFqSIbCx8xWuVgenoaQ0NDou3hhMJwfP1wXgOhvsFgEJ2dnZDJZNTaHE4RCDcuoTVxBa1YOfPRIJoX9fj4OAYHB2l1YO5e8a3wkcYmAjh56POt8+GE02jnHQ6ERpGVlUUznEQroAqtO1ycAJ/etWfPHnz+85/Hl770JSiVSmzfvj0qD1C4uQm1q9VqmrGEBN7Ozc1BoVCgp6cHRqORCptSxhfyxoSbP/eTP044xKtYiLVzPSbh8uKL9Zd0n+7dC/nLL4P94Q/x23MCOFeBmJ2dRUtLC2pra0WPDywIZoTuQQQzh8OBvr4+qNVqWmFbrNiV0PONUKlIpq1PfOITmJqaot60f//3f8evfvUrlJeXQ6vVYseOHThy5Ag+/vGPC+6BlPtWSKGMFCMhtp7S0lJJ9FUxBINBnDhxAiaTCWvWrIl5nAsJ50uglslkNMi+vLwcXq8XNpsN7e3tmJubg9FohMViQXZ2dsznaKXQipLVkZcXSeXgAoVMJos5UCka5WB+fh49PT2CgjR5GMZiiSZzkCqUkcBjUvE4HOdeqvudHF/Ius4dRyy4FIiuoJhUQZNlWQwMDGBmZgYbNmyQ9JCXYsEk51yIpiIlVoAI2VKsu0LtXGsp1woaz7qkWD3513pJSQlMJhP++c9/higGYoK0kCIWy9wYZiGYX6vVYv369ZDL5ZiamqLCJp/rvtRxAkLnnP+7mDU6VoyOjsJms9Gqx0sWUKhUgr33XrD33w+kpNDrmQEgB8Ceo/QJrZ/si9DfNPsRFqz/drsd7e3tCAQClFam1+upUioWJ1VeXg6DwYC3334bPp8vZB4+nw+vvvoq/vM//xMMw2Dnzp145plnQpQD7rzEwKczCRlPhMYI55XIy8uLqyJtIBBAfX098vLyokpzfKGDeK/PN1JSUlBYWIjCwkIwDAOn0wmbzYa2tjZoNBoaVxONEL1SaEVJ5WB5kVQOViFIIGwk+Hw+dHV1ib5gWJYVFE6E3P0ExIqlVCrh9XoFj8t/YfEDjxNhuQ/n0eALQlw6SzjBX2jNUoUqMh/iHVEoFFSA5LaLHVuq1V8sOFuKdZoPlmVDioLx20hfhmEwMzODjo4OlJWVUX65lLmHQzyKw3XXXYfDhw/jkksuWTTnSOvmHl/IGkvuC+6x+R4T8j3CdS8tLYXb7YbD4UBbWxtYlkVmZiaysrIEc6AvdeaiSHvLr58hBL63Z2BgALOzsxEzbcU6/0Xtl18ObNqEW9vacCIlBV6fD2SFevlCkTkuuOc/0vgKhQJarZYKZoR+NDY2hs7OTuj1epq2kij33OBzUptEKO6IYRj4fD56/K1bt+LBBx/E2NhY1BTScAgXKwIsvgYyMzNpwGws8Pl8qK+vR3FxcVx1ES5ELJdywIVcLkd2djY1vLhcLthsNjQ2NsLn8yE7OxsWi4W+Q8WwkjwH8SiqScSHpHKwCiHFcxAMBtHV1QW/3y/YLjWLj5jFkvs9IY8E6UsyiFRWViItLS1hQcJShWQp4/LHjmSlJevlC5d+vz/EOyJlXpHAf8Hz1xHPfkoV4Ox2OwYGBlBTU7PI28W10EbrhZF6Pghef/11XH755UhPT8euXbtw4MABmtI02rVForxwA95JDYPCwkIqXPHpQCzLQqvVIj8/HwUFBfD7/XA4HBgcHFxUpVmIJx/N3BPRTp4fQudAqD8pmMitQ8Ldo2iuScntMhlw77245I478NXt2/GLtjZMTk6iVKnED1gWCr8fEBCCovFGcc83VzAj9KOBgQGoVCpotVpMT0+jtraWUpBkMhm2b9++aPyUlBTceOON9G+VSoUrrrgCR44cwe233y55jvHQBPnXN0m7GSu8Xi+OHz+OdevWxR3IfCHiQlAO+EhLS0NpaSlKS0sRCARgt9sxPDyMs2fPQqfT0aBmPrUvGXOQhBQklYNVCIVCISr0Ax9U6nS73YLtiRAo+QIGnz/OsiwGBwcxOTlJgzb5QoWQkiFVuOev4XzFEXDXyxWMSK77kpKSkAJ23Aw+/DVL4Zvz21JTU9HX14eZmRmYTKawlTkToZSQ4PHa2toQoTaSIiZG8ZHiZRC7/o4cOQKfz4ePfvSjMBgM2LRpE9566y3ccMMNId9LpHBNvF6khgHxnEXaV7VajZycHOTk5IBhGEo/6unpQWpqKqUf8bN1LFWcgNDapLSTHP6pqakoLi6W1F+MyifFC7do/pWVwK5d+OiRI/joq69iLj0d/3HttcjzeIC33gJ27w7fXwBSYjW42Y+GhoYwNDQEjUaDs2fPhtCPNBoNnnzySTz44IMYGBgAwzC4//77UVdXF3Ltb9myBT/+8Y/R29uLK664ApdddlnM962UNfLHKy0tjdma7Ha7UV9fj8rKyrg8DxcyLkTlgAulUgmr1Qqr1QqWXagUb7PZcOLECbAsC7PZDIvFQrO2rRTPQVI5WD4klYNViEipTAnfXQjxCA9SLfeEWiOXy1FTUwO5XDg3v5iwz+fKcjnDRJiORLWJZU3R9iWYnJxEd3c3LQLGHZvv4eFTP8LFCQhZp81mM4xGI6ampjA8PIy5uTmagSUzMzOEJhTPuliWRWdnJy3Yxn1xJlpA5SsTfC41+dyzZw9eeuklapXds2cPXn755RDlIJHCMcnIQ7xeUvqLKXyE675mzRrMzc3B6XTSKs3Z2dnIysqixxCLkRD6W+jY4dqjOW/cHP55eXlR9Y8mRiJijAinMJrukUeQsm0b5hobkX7o0CLlIBKitciPjIzA4XBg8+bNVDl2OBwYHR1FR0cHdDodTCYTXnnlFQQCAXz1q1+FTqcLuQYGBgbwxBNPYHJyEq+99hpVaO+77z7R2BAxr4wU8NdQWFgYc3yby+XCiRMnUFNTE2L0WG240JUDLrjKa1lZGXw+H8bHx9Hd3Y2ZmRl4PB6Mj4/DbDbHFXi+1EjSipYXF+6VkUTMCEcrGhsbg9PpFOSQS+XNxzIH0pcfeCxmHQt3XH5chNALnevBELJUSvFGRDsvofbh4WGMjY0tytwSCy1AyAMjBJVKBZPJRDOwzMzMYHx8HAMDAyFBsWI5pCOti2EYtLS0ID09HWvXrhVUWKJZV7TrFuu/Y8cOPPzwwxgZGUF+fj4uv/xyPPLIIxgdHaUFqOIRjrnHttlsGB4eDjmvifJIkBzohYWF8Pl8cDqd6O7uhtfrhcFgoJV++QoZV2DkItaYj3AgVKqCggKYTKaEjw9EESNitQKf+ATkzz0HfPKT+MiuXfhbVxeub2gARkfBciqrJ0ox5MZYVFdXQ6FQ0PNhMplgMpnAsgtZk7j0oy1btuD1wVcnfQAAIABJREFU11/Hzp076bjPPfcc3G43VdwZhsHBgwfxqU99igrcUr2nUjxy3P5E8YwFs7OzaGhowMaNG8NW/l4NWCnWdiGo1Wrk5+cjPz8fLMvi6NGjmJqaQmdnZ0ixQCH65XIiSStaXiSVg1UIsYDkyclJDA8Pi/bjW97J/4Q+I/HHuYIKeamKVTxeCss9+X84S2U4CzWX4kMQTUCnXC5HR0cHvF4vTcsqFYnwVnAFapKTn2UXKtZOTEygubkZwIIgw7VKc48hpDD6/X40NTUhJycn6uDJRFNa+FCpVNi5cyeef/557NmzB+Xl5di5cycOHz6Mu+66a5ESw/3k/l9o3WTuLLtQh2NycpJSqRIxd7F2tVoNq9WK3Nxc+P1+TE1NYWJiAt3d3ZR+lJWVBbVavaR1JLj9haoeL3UcRESl8zOfAXPwIPDEE7jsxz/GnQ8/jN0AZIcOAecKjElZv9jzja8YdHd3w+Px4J133sE3v/lNaLVa3HnnnfjIRz4SMqZer4der0dJSQm8Xi9SUlLw9NNP49ixY8jJyUFWVhbNFqdWq+H3+yGTLSR0sNlsIYJ7vHQifv+0tDQUFBSIfj8cpqen8f7772PTpk0hCQhWK1aS5yAcyLVFgvXdbjdsNhuam5vhdrtpUHNWVtayrzdJK1peJJWDVQghz4HL5UJfX59oH77wwLXaSaEL8CkvxMVO+trtdvT19YVQMPjHFRo3Vit0IizzYmNzFSe+EsGyLAKBAObn52EwGFBVVbVIAF2qNUsZOy0tDampqSgqKoLX66VWaY/HQz0KJFUjH/Pz82htbcWaNWtClDvuizPeGIZY1kXaZ2Zm0NPTg8bGRtTX10Or1eL222/Hc889h8997nOC3qeIVml8YJVnGAbd3d0IBoOora0NUaDOB89foVBQZYBlP6jSfPbs2RD6EZ8iIuZ5k+KF4nok5HI5Zmdn0dbWhsrKSmppDNc/mvXF1Z6aCpwrjKapr0fZjh2wtbbC+sc/QrZ/f8RzL8UaT+ZBso399re/xdGjR+H1eiGTyfCd73wHAEIUBO44KSkpKC8vx+bNmzE5OYmKigrYbDYUFRVRmqVGo6FzKS0tlbwH0VLCFAoFSkpKYhIAnU4nzpw5gy1btlxw1ualwkoJ4o0WWq0WxcXFKC4uRjAYhN1ux+joKJqampCWlka9CmJ1PpYSSVrR8mL1Xe1JLFIOvF5vSMpSPuIVVolwxP0BPqgzMDAwgOHhYdTV1dEAWbk8tGCXFHqR1DkDHwT6iq0pXr49WSd/7V6vF2fOnIFarUZhYSFdG1kv8SDwlSkpiHfe/HOZkpKCnJwcVFdXY+PGjdDpdBgdHcXJkyfR3t4Ou91Or6OpqSm0tLSgoqKCBt5yzzUQqhhw1yyTyaBQKASVyESu++WXX8bo6Cg9ptvtxv/+7//i6aefDunv9XrR19cHl8tF+0ei3vh8PiqEv/LKK/B4PPT88y3Q3HPO34do1ybWLpMtVGkuKSnBxo0bUVFRAZlMhq6uLjQ0NKCnpwfT09MA4qPSkLgYwqVvbW2lqTrJ2sk1wj2/3OudfC8h63/nHWBuTrh9716guBj4yU/wkWuuwR+CQcjGxsDW14uOHwlc5Y94zVJSUmA2m3HkyBEEAgG6Vq/Xi2eeeYb+zf0hcwWAa6+9FkePHkV2djbKy8vx9a9/HSUlJSH359133x1irJHiKYwGxcXFYQvUiWFiYgJnzpzB1q1b/2UUA2D1eA7CQaFQwGKxoLa2FldccQUqKyvh9/tx8uRJ/P3vf0fbuWxgS0FTFEJSOVheJD0HqxBc5SAQCKCrq0s0QDmaOIJo+pK2trY2yOUfBB5L5frz+dQEpH+8tJtY+4Zr52auIZlJuFZKKRZWQHi9kWJC4rW+KpVKmqqRZUMrxQILil51dbXgwzqe+AiuZVqI2hHpRcS9jo4fPw6tVouMjAxMT0/DarXC4XDA4/FQQebYsWN44okn4Pf7wbIs7rjjDnzsYx8THZ8Ifc3NzbBYLMjJycH4+Dj+9re/4dprrxW0yvO9blLWzv1+NIGm5DsajSakSvPU1BTGxsZoUGx2dvaiKs3RCObj4+MYGhoKibHg9xeKBQpndCAQiwdatH67Hfj614GyMuCnPwV0utB2pRL48peB++/HttFRPDI9jf2pqQvUoosvFpyH1PuGH3ztdDrpHMmPTCaDy+UKGU9o/B07duDRRx/FzMwMMjMzodPp8MILL6CxsRFOpxPr169HMBhET08PvF4vMjIykJWVBb1eLyigRutttFgsMcUIkOJb27ZtWxZL8nLiX0E54IIYH3Q6HdauXQu/34/x8XH09vZienoaBoMBVqsVJpMJKpVqSeaQjDlYXiSVg1UIkq2IZRdSlvp8vkVCCJCYlKViIMF42dnZiwriRGsB53P9+X/zP4kgTqy14frHMy8u7HY7+vv7UVVVhdTUVAwNDUUVoyClXSwehDs/IYE6WsVBJluoFGswGNDX14fZ2Vno9Xp0dnYCAIxGI7Kzs5GampoQb4bUjE2R4gQsFgvsdjsyMjLAsiyCwSBkMhlVDBwOB/7rv/4LwMLLXq1W47nnnkNVVRVqamoE5z4/P4+mpqaQFLQ7d+7ECy+8ALfbjZqaGqxZs2ZJ185fN7kG+IoIAVH0TCYTGGahQB23SrPRaBSkH4mBn642EeAqQpGeMXT9ZjPw2GMLCsLdd0N24ACYcxQ4Osa5wmiKp5/GNR/6ENp7e1Hx1lsL3gaepVvqfUE8Brm5ubBYLAAW7oHi4mJ0dXXR86jRaHDttdfS/mL3RlpaGrZt24a33noLe/fupXPfsGFDyPdImtvJycmQOJPs7GwYjUYqlEWjGKSnp4fUWJGK4eFh9PT04JJLLhFNZLCasVqUg1it/iqVihofWJbF5OQkbDYburq6qMeBBDVH6xkWQzLmYHmheOihh8K1h21M4sJFf38/tQCHewFz6Q98fm24PuEeMkSgkslki6qUxsupF3vwcC2VZL3Dw8M0Sw0QWlMgWoqL2LxIgOrExASqq6upRc1ut8NgMEClUkmmZklp53sVInkWuC807roJxOZG8terVCqUl5cjMzMTVqsVRqMRXq8XIyMjGBgYoFlWUlJSRIX2cOuKJJwJ9Rdbd25uLv7617/C6/UiEAjA5/PhYx/7GDZt2gSZTIZ//vOfePfdd6FWqzEyMoKMjAz4fD6kp6dj8+bNi+Y+MzOD1tZWlJWV0cDbmZkZPPHEE2hpaUFTUxPefPNNKJVKrF+/Puq1Rbt27lrD0Y0IjYuMo9VqYTQakZubC51OB5fLhaGhIQwPD8Pr9UKhUECtVi+y5jMMQ+lXVVVVIYpBNNdsrO2C3qiiIrCVlZD95jdg/v534KqrAI6SI5PLIVu7FoqXXkJJaSmeHhzENZOTkOXmApz4H6mGEY/Hg6amJhQVFS3KyrR9+3Y0NDRgdnYWgUAAGzduxDe+8Q26T+GeLTKZDIcPH8buMKlWyb1LAs9zcnKg0WgwPT2Nvr4+jI+P0/NHnjNkbC6NjVwTSqUSZWVlUWfdGRgYwMDAALZu3fovqRgEAgG0tLQgJydnxVOpGGahNk08Be9kMhm0Wi1MJhOKiopgNpvhdrvR19eHrq4uzMzMQCaTQaPRxKVQHTx4EFu2bFl11bYvMHxLrCHpOViFkMvlGB8fF+Xr8S12kSzNYtZ5Po0AWLDO9vb2oqqqCi0tLVHPO55g20h9w1V9FbJQ83/nWjIJD7mrqwsAQirDSplPNPOO1bsTjvbBH5t7bv1+P5qbm2EymUKUK5ZlFxXvcjqdGB0dRWdnJ9LT0yl9RaVShRX+4l23UHtlZSUef/xx/OlPf4LL5cIVV1yBrVu30u/pztFQ5HI5rFYrFZoyMzMXUZtIbYr169eHWNgPHToEm81G7y2VSoXnn38eO3fupFSNpVib1PZI9DWtVouioiIUFBQgGAzC4XBgaGiIVmkm5y8YDKK9vR0KhQKVlZWC98FyrA8AZJdfDuaHPwS++tWFIOQnnwTOVS5mWRayykoEd++G+c03MZCeDnd+PlIOHQJuummhv4hHhguGYWhWJlLgLmQOMhlycnLw4osvYmJiAi+//DICgYDktLY7duzAI488AqfTGRLcH24PuFQPkv2IPG89Hg+lH5E0t/xnWklJSdQUkJ6eHthsNmzduvWCzom/VPD7/aivr0dhYSH1Gq1kBIPBhKdkJdW1i4qK6DPFZrOhpaUFWq2WehWiraWRpBUtL/717vZ/ATidTjgcDpSUlETdV8xiRz7FBB9iQXc6nairq4NarQ4JxpPCQV6KOAKWZaFQKGKmMYlZrok1yWg00nSAXCGDG4gZqwcmXiEqHMQUB5fLhZaWFkqjEVOkiHXSbDaH1FOYmJhAf38/radA0mzy+y+V4lBSUoKvfOUrgu11dXWwWq0YGhqCSqWCy+VCWloarr76avp9lmVhs9kwOjqKmpqakLnLZDLqEUtPT8fU1BStODo4OEi9C/GsbanbuXunUCjo+WMYBtPT05icnERXVxf8fj9Nwcm3QJNxCKQ8HxK5PpZlgW3bgB//GLj3XuBznwMOHAC41Xm/8AXIjhzB/2cwoMFsxqX19UBPD1Bait7eXvzyl79EX18fLrvsMnzqU59alEGNxA+RwoVCigT53Ww24/rrr8fdd9+Ne++9N6RSuNga1Go1brrpJoyMjCxSDqQaFriKejAYXJTmltDHVCoV9RpFg87OTkxOTuLiiy9esTn+44Hf78fx48dRUlISExXrQgTDLG29Bu4zBViIw7PZbDh16hT8fj9MJhOsVisyMzMjeu2TtKLlRVI5WGWYnZ1Ff3+/aHu81nehdlLxWKFQ0MBjhgnNZhPJG8H9ne+ViNV6TgSYRFvm3W43WlpaUFRURAN4ybyF1sL9XzjqTTQxCvF4FPjHIpienkZnZ+eiSs5CYwsdm1g1iXBFstsAoIIKf1z+PJZScVAqlfjhD3+IF198EadPn0ZpaSn27dsXUmhqcHAQMzMzqK6uXmQpZVkW69evR2NjI1JTU6HVahEMBhEMBmmBIT4FjHsdcM89l0sfDSLtTax7J5fLYTQakZ6ejpmZGZhMJsjl8kXnj8SZhIOYRT5WvrMoNm8GfvazhSDkcwqCPDd3YY1WK7BvH6qefRYPzs1hu0IB2aFDGLntNtx5551wu91gWRa9vb1455138MILL1CF1+l0oquri8YPcecutoclJSX4n//5n4jZmbhjffnLX45p2ULXODfNrUwmw+zsLOx2O5qampCeng69Xo/U1FTodLqI549lWbS1tWF+fh6bN29eFVz7aOHz+XD8+HGsWbMmxHu60rEUnoNwIAUd16xZA7/fT41HjY2N0Ov1sFgsMJvNgnS1ZLai5UVSOVhFCAaDGB0dFXX/RlIMYrFie71etLS0wGw2i1pXpHgjIgUlCr2gIlEoSFss+wEI7wkRoMvKysIW/xGqNcFVesLFMHDTnXL/z51PohWH8fFxDA4OLqrkHO3YpD01NRWpqakoKCigVX5JcDy3yq8QZY0vvBBBOhFWc51Oh7vvvntRG8Ms1DAgCoCQACWXy3HDDTfg6NGjsNvt8Pv9UKlU2LdvH6Um8b0xYgqfkFLM/+QrjZHu0Xjh9Xpx9uxZqvQCoFWaSUCz2+1eRF/hriOc102MKsP95I8V0UhQVwf84hfAPfdAftddYA4cAAhH+dOfBvuHP+C2mRnM1tYi47XX8EogAK/XS4/h9/sxMDCAM2fOYOPGjRgfH0d/f39I/BB3TuGuL/L8E6Nr8veIPL/4eyG2ftE9EBifCGVlZWUoLS2Fw+FAW1sbXC4XLXSVnZ0tmCmqqakJDMPgoosuikmBXenwer04fvw4ysrKoi70eKFjOes1EA9Wbm4ujYe02Ww4fvw4ZDIZLBYLFAoFiouLaTKIaD0Hv/3tb/HQQw+htbUV9fX1i2LJCIqLi6HT6aBQKKBUKtHQ0JCIJa4qJJWDVQSFQoGysjIAoNlF/H5/2J9AIBDRhS32Qpqbm0NrayvWrVsnmhovHksvt6/Qd/iKAV/QUCqVIdbcaLwRQu02mw3Dw8Oorq6GVqsNq9CIzTnSscWEAkBYkQpnoRQSJoUE2MHBQUxNTaG2thZqtVpyDIPUdZEqvzk5OQgEAjTTRWdnZ0iaTbVaHZZLz50H95O0C3lrpMw9EAigra0Ner0eBQUFoooBwzAwGAw4cOAA3n33XTgcDmzYsAFlZWUJiROQEqAsdr4jKQ2Rxg/Hr1er1cjLyxOlr2RlZVFPQ7THF7PI89dDqIGCRoKaGuDAATCf//wHFKPCQiA9HbK770b1Y4/huM+HrU4nxltbaW0CMp5cLofD4cDo6ChGRkZQW1sbU3pGbhA3KSbIb+/p6cHbb7+N9PR0fPjDH4bBYKDtUu4vvkJB90Dkml+zZg1SU1ORlpaGwsJCygkfGxtDc3Mz0tLSYLVaYbFYoFarcfr0aajValRXV/9LKgYejwfHjx9HZWUlpcasJiw1rUgqZLKFjHgZGRkoLy+H1+uFzWbDN77xDbz77rvYtGkTPB5P1MaQ6upq/P73v8f+/fsjfvevf/0rNYIksRhJ5WCVQi6X0ywWkRAMBiMqEX6/P0QQJxWPiaAsBJJSVexhFA9nPpI3grxASQEnLojQLPaSFRJU+vv7MTc3RwWHSAK02NoSHUfAVSTCWW6F+OIkoJplWdTU1ESMzQgHqYqDQqEIqadA0mwODAxApVLRNI187wV3X6TSsLjnmBtMzu37/vvv46WXXoJOp8Ntt90mKBDxx9ZoNLjqqquiXnui2oUUPiF6FvnkX+/8/ZudnUV7e7sonYwfp8Cv0ux0OnH69GnI5XLBKs1xByDLZJGTCVRUAP/938DnPw989rOQ/fd/Q1ZaCtx0E7zPP4+85mbIMjNxtd+PYxoNPB4PgIV7wO/3Izc3F2NjY6ipqRH0NEazhl/96leoqanBbbfdFtJ+6NAhPProowgEAlCpVPjZz36G5557DkVFRZLiDMi9HsnLSlBQULDI8srlhLPsQrrpsbEx1NfXY25uDgaDIaQy878S3G43jh8/jvXr1y/KTLVacL5pRVKRkpKCwsJCvPDCC/B6vfjzn/+Mr3/967jqqqtgsVhw3XXX4brrrkNxcXHYcSorK8/PhP8FIIugmS2dDzuJJcWxY8ewdevWhBYoIS/S1tZWjI+PU/qFkDeCZVk0NjaiqqpKcA7xZuGRQoFqaWlBcXHxohekFBoTd80dHR1QqVRYu3btIms1nztOxu7v70dqamrISyZW6paU/tGOHQgE0NraCoPBgIKCghDFQIgrzxVeItElYp3b/Pw8HA4HHA4HWJalPHedTrck+/anP/0JP/jBD6jgrFKp8OCDD2LHjh30O+EoIlLWdqG3O51O9Pb2oqamRrCwVThhlD++x+OhyRC8Xi+thxGO5y6FKhXVGru7FxQEll3IYrR2LeT/+AeY++7DXGUlUtvb8diuXTh85AhYdiGxwP33348NGzagoqIiRHCKFGdAwL/+jh07hmeffRZPP/007e/1enHNNddgfn4+pO+OHTvwxBNPxP1s4LcbjUbJCSmCwSAaGhpgMBiQmpoKm82Gubk5ZGVlwWq1Iisr64IUKBMJohjU1NTQGKTViPHxcUxMTCxKvXwhYvPmzbTa+2uvvYY//elPsNvt2LVrFx5++OGwfa+44gr84Ac/EKUVlZSU0KDo/fv343Of+9xSLGElQNQ9mPQcrFIQznsilQPCR1WpVLjmmmvC0gj8fj9mZ2dRXFwMlUol6o2I1roezUtUjOMslTbj8/nQ0tICk8mEvLw8QSGBK/RwgxG5vxMk8uUfDfjz9ng8aGlpQX5+PsxmsySuvFBchxC9R4wvL2VuQnEKAwMDmJ+fR0ZGBrKzsxdViY1136anp/Hkk09CqVRST1AgEMCTTz6Jyy67LGR+YlZ5viWe/J7IuIClVAzGxsYwOjpKvWFSri8+rYlLg9NqtZRTTOhjo6OjaG9vF63SHAlRn981a4CnngLuvhvYvx+yX/wCzGWXIVBXh/SuLoBh8J9lZfjsPfegq6sLX//611FRUYGKigrR+5urNAt5HPnK9NatW/Hggw9ibGyMctbHx8cF19Ha2poQzwrfsyU1j30gEEB9fT1yc3OpVbawsBAMwyyiH5GUlKutOvL8/Dzq6+tRW1srmFZ2NeFC9RwIgTy7SktLcc899+Cee+6By+XChz70Ibz66quLvv+d73wHN954o6Sx33nnHeTm5mJ8fBwf/vCHUVFREWIUSiKpHKxaKJVK0UDdWODxeNDQ0IC8vDxJFimVSoW0tDTodLqwGQfCUZoCgUDI75EglBGJ+3c0ArbL5UJraytKS0thNBolvcD5+x0MBkWt7OSTq0AIxUZImXc06yIpGgm3PB5KjBBXXkiQ5nLFxSzI/H4kTaPVaqU8d1KRMz09nVJbwkFs7oQSNzc3h9TUVMzPz4NhGKSlpcFms0Xsz1V84uGISwmwTqSiwcXAwABmZmZEaTRix+fT2MTmr1KpqDBJ6GN2ux0DAwNQq9XIzMyE2WwOa7yIViimKC4Gnn4a8v37wezfD/z851B+7WvA7bcv1EP44x+R9fGPw2k0oqKiAiMjI6irqxM8hhBNL9wzhqz9yiuvxJEjR3DnnXeCYRhYrVbB66CysjKuIHv+HOVyOdasWSMp6JSk6iwuLl5UaEoul8NkMsFkMlH62NjYGBoaGsCyLMxmM6xWK/TnKlSvVLhcLtTX16Ouro6mIl7NuFBiDmJFWlpaQoKHSQYqs9mMvXv3or6+Pqkc8JBUDlYphLLlxIqpqSmcOnUK1dXVUXExw2USIlAoFFAoFBGtUSzLSoqL4AovXKpMNNQTklmHm+M8WgGa+z+xWAApAiKXM8/fDzK21HVxC9SRlJSRLM+J4MrzM7QIzY3/P2KNlclkVFDJzs4GwzCYnZ2Fw+FYVE+BG6cgNvfh4WFMTEygrq4OVVVVaG9vh0ajgdPphEqlokJiPAqZ0+nEsWPHEAgEcPnllwveM0KKLP+T7IPQ3sU6P5Zl0d3djWAwiKqqKlEhMhEKKbedW7zL7XZjcnISzc3NYBhGkH7Evb65fxNEvHYLCsD88pcLHoQvfAH46U+B3buBN94A7Hb0Hj4MbV0dbrrpJvzlL38RrFQcD9Vn586d+PnPf47bb78dwIKx5oEHHsCjjz5KM6gplUp85StfEfTACa1ZcJ28ORYVFUmy7JOMPOvWrUNOTk7EY5Dzt27dOvh8PppQYHZ2FkajEVarFdnZ2StK8JydnUVDQwMuuuiikMDw1YzlzFYUDfhe90TC5XKBYRhaLf4vf/kLHnzwwSU51kpGMuZglaKxsRGFhYVxW0NGRkbQ0dGBzZs3R106/vTp0ygqKjrvFhnicThz5gwMBgMyMjLCUpq4L/mRkRGMj4+jqqqK5l6OJkaBYGxsDIFAgLroxZCoOAIhAYMoZyzL0nWtX7+eWmsTGcOQ6HYpiguwwBUmcQpE0CT5+rlgWZZWkq2oqIBcLkdfXx/uu+8+uN1uTE1NwWg04qmnnkJBQUHMa29ra8N9991HFVWlUonvfve72LRpk+S1S81cxN0HgnDB8AzDUGWouLhY9OV7Ps9tIBCAw+GA0+mEy+WCXq9HVlYWTQ0r1JccI5JXg2VZYGxsIQbBbgf+3/8D+3//LxAIwP2RjyD14Yfhcrmwe/duHDx4MCRLU7xrDAaDuPbaa/HMM8/QIokA0NfXR7MV7dy5M2w65HCUNn5MEABkZWWhsLBQdDwCt9uN+vr6hGTkYZiFKuljY2Ow2+3QarU0+9GFTD+amZnByZMnsWnTprDnYLWht7cXMpmMUsguVHi9Xlx55ZV49913o+r36quv4ktf+hImJiaQkZGBuro6vPHGGxgZGcFdd92F1157DT09Pdi7dy+AhefPvn378I1vfGMplrESIKqBJZWDVYqmpiZYLJaYsy6wLIuOjg44nU5s3rw5ptiFs2fPIicnZ9nShbW1tSEjI0M0VzUJsPb7/fD5fDh79ixcLhfKy8vBMEwIrUkI4QRYm80Gv9+/yF3PxfkIQGZZFj09PfB6vSgvL6cUEn4sBN9CfSErDmLtfr+fCprcOAWdTofOzk6o1WqUlpaGCJ0+nw+nTp3CsWPHMDw8jMcffzwuHv/+/fupAE68XWazGS+//DL1hJzPAGRyTG5Fb1KwDYitCF087eHAMAtVmp1OJyYnJ6HRaGj2Kn6l6nDHIFnS5HL5wnU+MQHs3w92dBSODRuQXV8PVqsF8+abkGk0OHDgAK655hqsXbsWQPyKK/nOY489huzsbHzmM5+Jeoxo74G0tDSUl5dHtLYSfv1SBd4S+pHNZkMwGKT0I25Nk+XG9PQ03n//fWzevDnqqtErHd3d3VCr1SEK64WIyclJ3HrrrThy5MhyT2W1IxmQ/K+GeGhFwWCQ5rveunVrzG7IeFJjJgJSXrApKSlQKBRobm6GxWIRfMHyKU1cpUGI1gQsrN3tdsc8t0QI58FgEG1tbdBqtaisrAwJqOQfW4iywg8+5X5PbA5SaE5LpTiQIjvcOIWxsTGcPXuW5uPn3xNKpRJbtmxBRUUFdu/ejZmZmUU86kjKEhc9PT1Qq9Vwu90IBoNIS0ujXqRwKXCBpRHMWZaF1+tFc3Mz8vLyYDabRfePCNNCYyQKkbxwxGvAsizNXtXS0gKWZZGVlYXs7GxotdqQ8/OXv/wFBoOBPquCwWBIoDSysuD5yU/A3H03sk6dAqPRAG43ZH/7G3Dttfj85z8fEhvCpbRx4wykCrek386dO/Gd73wH27ZtQ0lJCc2alugAZKVSidLS0ojzIzSapeTXp6enY+3atVi7di18Ph/Gx8fR3d2NmZkZZGZmUvpRNEHpiQShyG7ZsiVqT/hqwEoJSI6lAFoSiUWO81cOAAAgAElEQVRSOViliFU58Hg8OHHiBAoKCuJ2PSYy7iEWSIl5cLvdOHHiBEpKSkStKTKZDGq1WrDEOx9EcSDc9ry8vEXKRCAQCBtgnYjMRCTTksViCeEURyOYSA2OFuLLEwhSPSLMXcrcIrUrFAqkpaWhvb0dFosFVquVZj/i1lMg1AedTofLLrsMb7zxBm655RZBAVkoToAvkJWUlKCjowNqtRqTk5NQq9WwWCxQKpVLGmAsBo/Hg6amJpSWltLaBGKQEmDNFZL5AfVAfJW73377bbzwwgvw+/24+eabccMNN9DiXT6fD1NTU/j/2Tvz6EauMu0/kryv8iJLcttu7+722m1btrsz0AkwBJJ0EkICJ2TIQGZgMkwICZCwTM5A2BkyOTAhJGEIhDAQMoEEknSzHAidhXQsyfvW7fa+qSRLli3J2lX1/dHfLWRZtiVbS6lUv3PmhGnbqqsqqeo+977v88zMzMDpdG5JabZYLPjZz36G2dlZ9PT0bLtvbW5uYmJlBfWPPgrmc58DpqYu/+CnPwWuvnqbAPD//BMCBUPgtQ/sKWIYBm+++Sbm5ubwiU98AgBw//334/Tp0wduQA6ksrJyz3sTWS2PZRlNWloaysrKUFZWxpYf6fV6XLhwARkZGWz50U45OZFmbW0Nw8PD6Orq2tUkg8+QHTWuY7fbk/YacQVBHPCU/UzM99t4vBOhTM6jyV47F+T9tra2RmyLnTQa5uXlweVyhVTStFeCtT+hCIdApyVCtFbtQ22OJr+z38bLcMa2vr6Or33taxgcHIRIdDkp9stf/jI6OjrYPoULFy6wfQolJSW49tpr8aMf/Qg333zznq9Pxk3GTn5+7733sj0H5PN333337dpYvtNuzl7H3+vnxJmqvr4eUql0z2uztLSE/Pz8PYPQAkuS9hq//45EoP0r+e+LL76I//zP/4TL5QIAPPTQQ9DpdLjzzjsBXA5JIuFd/inNfX19eOKJJ2A2mzE9PY1HH30Un/70p9maYv+At9zcXDCPPQb8278BFy4Ak5PA0hLw/0v/wl2x3004a7Va/PKXvwRweaIjFovxjW98AyqVCnK5POjfh0LgGEnJzm6YzWYMDQ3FdbVcLBaz4YfA5c+mXq9Hf38/W34kl8tZB7VIYzKZMDIygq6urqRdkTYajVhdXWXL57jM5uZm0l4nriD0HPCU+fl50DQdchDOQRqPd2JmZgYSiSRkz+1IMz8/D5/PFzTxU6fTse83GisUJpMJKysraGlpOdDrMAyzaxlTYPCc2WzG1NTUjmm3OxHvPoJgtfL+//UncEcj8G/X19fx2GOP4c9//jPrYOR0OlFbW4snnnhiy2t5PB6YzWasrq7CZrPB4/GgqakJ+fn5Wyb04bw3k8mEV199FWtra3jPe94TVoOzv3jyX5XfqUdgp/Gtr69jamoKjY2NyMnJ2XX8Y2NjuO+++2C1WsEwDN7//vfjnnvu2dL8G24JnM1mg1qtxjve8Y6QdkyuueYarK6ubnm/GRkZeO2111hxEWwM3/zmN/Hb3/6WTWIXiURITU3FCy+8gJSUFExNTaGpqQnZ2dl/+3ubDbjtNmB5GejsBB5/POKf34ceegjPPfcc2++RkpKCtLQ0fOYznwnqxR5MNJPzEChACcQ9aLfJtNFoxOjoKKcnxR6PBwaDARRFYWNjgy0/kslkESk/Iuegu7s7ZrsUXMNoNGJsbAzd3d2cbhQnvPnmm3jmmWfwyCOPxHsofEfoOUg2JBLJjo20/vg3Hl9xxRURDU2Ld1lRsHPAMJetHA0GA06ePBnR9+uPWCyGxWKBzWY7kNgik51Qxjk/Pw+TyYT3ve99SElJ2SYe3G43PB7PtmsSy3KfUH8eanM0+TmZyBsMBiwtLWFsbAwpKSlwu93wer3Izs7G7OwsjEbjlgb5tLS0LSvSGxsbWF1dxfT0NLKzs1FcXIyCgoJdswACx15UVISbbrqJ/Xk45zZYKddOvR3+/yXuPSKRCAaDAQsLC2zq8W7n3uPx4JOf/CRsNhv7Wv/3f/+HP/zhD0hLS8P111+Pj3zkI7tO0nZ6fw8++CBUKtWeZSwikQibm5vs8YnjEjEKyMzM3NH2dXBwEDRNbwl9FIvFeOONN9iEX6/Xy/YhAABycoCf/xy4/37gP//zwH0ywSguLkZqaiprWwpcvkY7hWyFMwZyT9irz4CU8PT09HB6QpiamopDhw7h0KFDYBiGdT+6ePEi0tPT2fKj/Ygbg8GAiYkJzp+DaJJowgAQyoq4gCAOeEooE3Ofz4eBgQGkp6cfqPF4tzGEIlCiRWBZE03TGB4eBgD09PREtfZSKpWirKwMo6OjcLlcrGtHNLbNicBbX1/HVVddtedqW2BJ0247E1wUDv6Q0h2GYbC0tIS1tTU0NzcjJycHFEUhJSUFNpuNXTFMT0/fdt3Je5BIJKwVKsMwsFqtW/oUSJ5COA/YaDUg77STsLy8DIPBgNbWVqSkpGzZfQj83JHvA5mMk++Kz+eD0WhEamoqnn76aaytreH+++8Pa4w5OTno6urCK6+8smtqKbm+V1xxBf7yl7+wYxCJRGhqatomDALfe1NTExYWFiAS/S2VnJSptLe3Y3NzEzqdjm00J9dXnJMD0WOPBT2H4RLsM3r69Gn87//+L2w2GxjmsqVtUVERTpw4se3v9yM+qqqqdv2er6ysYHp6GidOnAipV4oriESiLQGHm5ub0Ov1GBwcZJ2/5HI5CgoK9ryP+osj/wyUZCIRhQEglBVxAUEc8BRi57cTDocDWq02Io3HOxHvngP/h7bb7YZWq0VJSQlqamqibqsnEolw+PBhHD58GF6vFwaDATMzM7BYLCgsLGQtXg8qUGiaxtDQECQSCVQqVUivR1ya9npg7lTSFOzfgk1uYiUcyG6Q1+tFc3MzxGIxbr31Vnz9618HTdPIz8+Hx+PBqVOnkJuby77mXnXyBQUFkEqlqK6uhsPhgNFoxOTkJLxeLwoLCyGTydgwuWBEuwHZ//UZhsH8/DxsNhtaWlrYEhv/nYhgNfKk3Iacx8DX9nq9eOmll3DvvfciLS0tqKvVTlxzzTV49tlndxQH/n9///33Y2VlBVNTU/B4PJBKpez12+39f+xjH8Nf//pXOBwOuN1upKSk4MYbb0RXVxdSUlKQmZnJNmJbLBaYTCbMzc0hPT2dvYb+eSY7lfbsdC13OgdFRUV46qmn8OSTT2JychIqlQof/ehH91UmE3iMQ4cO7bobubi4iIWFBfT09ERtZzRWZGdno7q6GtXV1fB4PFhdXcXc3BwGBwdRUFDA2nUHvk+dTodLly4lnDiKJIkqDADBrYgLCD0HPMVkMmF5eRmtra3bfkYacVtaWqKaQaDX62EymdDY2Bi1Y+zG6uoqDAYDKisrodFo0NDQsGcaaLShaRomkwk6nQ4mkwl5eXlQKBQoKSkJ+0Hu8Xig0Wggl8tDsjKMJj6fL6QGa/+V4YOsqgfatWZlZaHSL9hLLBbjlVdewc9//nNsbm7i7//+73HbbbexE4WDCBOPx8M2xNrtdhQUFKCoqAhSqXSLOAtWIhTK64f7c4ZhcOnSJQBga9DDEVb/+I//iKmpKXi93i1uTzRNs+frz3/+85YJhn+zf7AGc5FIBKfTiauvvhrPPvvstrCtna7v0tIS3njjDbzyyiv44Q9/uOP4/V/DarXiD3/4A2ZnZ9HU1IT3vOc9EIvFu54Dh8OBtbU1GI1G+Hw+FBYWoqioiE1E9z9HwY5Lfk6usX+vxG79MIGE28sglUpRU1Oz4+/Pzs6CoiioVKq42YXGAtJfRVEUVldXkZqaCoVCAYVCgfX1dUxPT/NCHO2XRBYGAPDkk0/C5XKxTl8CUUPoOUg2diorWllZwaVLl2Ji5xbvngOxWIzNzU2o1WocP358SwJqPMckk8kgk8nAMAw2Njag0+kwNTWFtLQ0KJVKKBSKPW/odrsdGo0GdXV1KC0tjdHod0YikUAikew5boZhQhIRu+16kR0Jj8eDsbExlJSUbDkH5OdXXnklrrzyym1/f9CJeXp6OnsNaZpmhcLU1BSys7Mhk8kglUq3Tc4C7TB3cu4JxzWHiKPs7GwcPnw4LGFAXuvRRx/FY489htdffx0URUEikbC7fgzDoL29fct1FYlEW77XgZNfMr60tDRcddVV+OMf/4jbb7+d/d3d3KrKysrwvve9D0NDQ2wj717vIScnB21tbWhtbQ1ZHGVnZyMzM5O1GjaZTFhaWmJTmouLi5Gfnx/UE97f+nS3RnEioPz7QfxfI5Q+A//XTU9P33WX99KlS1hbW0NXV1dCeNkfBJFIxJaIAZfvhxRFobe3F5ubmzh8+DCsVmtI5Ud8I9GFAXD5eiZTcjUXEXYOeAqx8Ovs7ATwt7p0s9mMjo6OmKyomM1mLCwsoK2tLerHCsbFixcxOzuLU6dOJYRLxebmJiiKAkVRoGmaXQkLTPE0m80YHByMapgRF9itF8JisWBgYABlZWXb7FqjVee/188ZhsHm5iaMRiNMJhNbZ15cXMw+pEN5/WD/m7y+/996vV6Mjo5uEUcHfX///d//jXPnzsFgMMDj8UCpVOLHP/5xWOeYpmmo1Wqsr69jaWkJP/vZz1BWVoZ3vOMduO2225CVlRW0j8A/hMz/3wPLo/wn/jRNs42rVVVVIQmD3cZPxJ7ZbN41pTla7lyB/9v/HDQ0NAQttWAYBhcuXIDdbsfx48cTwsc+GiwsLGBxcREdHR3sroLZbIZUKoVcLt/X7myiwQdhAADf+ta3UFNTg1tuuSXeQ+E7ws5BspGSkrKlwXBgYAAZGRno7u6O2UpKvHYOyMNybW0NRUVFCSEMgMurmTU1NaipqYHL5YJer8f4+DgcDgdkMhmUSiWcTicmJyeTIsiHZEYEXr+NjQ3Mz8/jxhtvREFBwbaSpp1ExW67EaGyV4lITk4OcnJyUFlZCafTCaPRiIsXL7KlK8XFxcjOzg76HQycMO52LJJ6XFFRwZbskElkYC9COFx//fU4e/Yszp49i9HRUczPz28RBntNei0WC+644w4YjUZ4vV44nU4AwNzcHJ5++mmMj4/jv/7rv3Z873uld5PfI6vuExMTkEqlbIDhbqVcoUD8+ElTeqgpzYHvZa8G490cqYKdh4qKih2FwdjYGLxeL9rb25NulZwwPz+P5eVldHd3IyUlBUqlEkqlEgzDsEnpU1NTSE1NZUMR+Xb/5IswAISeAy4giAOeQibmpPG4oqIi5nkD8WhIJkIoMzMTbW1tmJiYiOnxI0V6ejoqKipQUVEBr9eL1dVVjIyMwGq1orS0FDabDRkZGbwvHwjEYDBgfHx8S6BTJEqaSGq12+2G2+0O+vfhNhhnZGSwCbEkT2FhYQF2ux35+flB+xR2gxzfbrdjfHwctbW1W8LNdpuUkhX1YOUt5L8SiQSVlZUoLi7GxMQETp48iZMnT7K/G8pq+Y9+9COsrKyApuktYszn80EikaCvrw86nS5o7084k2qya0ISwP3PQSgr8oG7EcHeo0gkQnZ29paUZrPZHDSlObDXZDfC7UMggiTYuRgaGkJKSgra2tqSVhjMzs5Cr9eju7t72/1QJBKhoKAABQUFOHr0KBwOByiKwsjICJxOJ2QyGRQKBQoKChJ6x4VPwgAQrEy5gCAOeIpEIoHL5cJbb70V9cbj3cYQS3HgdDqh1WpRVlaGyspKOByOsC0CuYhEIoHRaEROTg6uuOIKdiVsfHwcOTk5UCqVkMvlvN8yX1hYwPz8PE6cOLEva0KRSIS0tLRd3Uv+9Kc/4YknnsAzzzwTUm9EKM5HwNaEX1K6YjKZMDMzg6ysLMhksl3zFMjrWywWTE5Obgu5C6WMZbfvIhHyIpEI733ve/G73/1ui+1mKBNeUk4U7Djk7yUSCSwWy76MAcik2u12Y3R0FOXl5VuS3EPZddhL3JD/BjYZA2BXneVy+ZaU5unpaWRlZbGT+N0Ee7jlSJmZmaioqNj2ezRNY2BgANnZ2WhoaEhaYTA9PQ2j0QiVShXSQklmZiaqqqpQVVXFLrosLi5iaGgI+fn5+zaHiCd8EwaAYGXKBQRxwFN0Oh02Nzdx1VVXxU2Bx1IcWCwW9Pf3o6mpiZ0wxNtKNRJ4vV709fUhPz8fzc3NEIlEKC4uRnFxMWvPSFEUzp8/z26nKxSKhCmlCgXixmM2m3HixImourB0dXXh5ptvhtlshkwm2/M8BmZG7OTQ5L8bQcKw/EtXyCRFIpFs61MgE8a1tTXMzMygubl5yyQgEvXv/s5HV199Nf7nf/4HdrsdGRkZO66yB7P+rK6uxszMzLbyprS0NPh8PuTm5gZ12wn1PTidToyOjqKmpmZLv00473EndhMW5BhENKSkpGwxFrBYLDCbzRgeHmavLyk/2u8YJRIJqqurt61o+3w+aLVaFBUVoba2dtf3xGcuXbqE9fX1kC2cAwksP9rY2ABFUZienoZEImHLjw4SYhlt+CgMgMvPc0EcxBdBHPAMhmFw8eJFrK+vs1vi8cLf7jCakFKTjo6OLc27sTp+tHA6ndBoNDh8+HDQ1UORSIT8/Hzk5+ejoaGBdewYGBiA1+tlSy5yc3MTdmWRpmmMjIwAwL4nAeGQl5eH6667Ds888wzuvvvuPX8/nMyI3XoiSkpK4PF4YLVa2TwFj8fD1r+TMK/W1tYtOx+RSPcNnAQXFxejpaUFw8PD6Orq2vXvAjMAPv7xj+PNN99k3xeZUKekpCAnJwcPPfTQlvGH4tpDJtWbm5uYmJhAfX39FieT/bzHQMIp9QnWz5Gfn4/c3FxUVFTA6XRibW0NU1NTcLvdrFDIy8vb0aEqGIcPH9424fN6vdBoNFAoFKiqqtr1PfGZixcvwmq1oqOjIyL3BJFIBKlUCqlUiiNHjsDhcECv12NsbAwOhwPFxcVQKBSXA/Q4Un7EV2GwvLyMV155BZ/97GfjPZSkRnAr4hFer5ett29qasKrr74a1MoxVjAME/UxzM7OYnl5GSqVatsEjaZpvP766zh16lTUjh8tgu2EhIPb7YZer2d3kEhDc2FhYcIIBbJrUlBQwFpUxoI//vGP+OIXvwitVhuT4wVCxIPdbmethy0WC2QyGQoLC5GTkwOfz8eWAUXDfYnYiO5nV4KiKLzwwgswGo1417vehbq6OlitVlRUVGwr/QicdIvF4qC9ARsbG7h48eK2cqqDvMfd3kM4P9/t9b1eL8xmM9bW1mCxWJCbm4uioqJtJWSB9rbFxcVskzXB4/FArVajoqJi28+SBWI24XA4cPz48ZjcE3w+H1ZXV6HX67G2tobc3Fy2/CheAWt8FQYUReG6667D9773PVxxxRXxHk4ysOMXSBAHPCFY4/G5c+fiKg6iOQaGYTA6Ogq3241jx47tWG/KhXMQLqurqxgbG9u2E7JfyMONoiisra2hoKAASqUSMpmMsw3NLpcLarV6x12TaOLz+XDo0CF85jOfwfHjx3HllVfGJVCKYRhMTEzA4XCgra2NtWck/SdyuZx1EtqtnMnj8QR9/UgGsQXjoJN28jtra2uYnp7eUk4VrKRpL9vTaLyHUH7Hf0wkpXltbQ1paWkoKiraktIMIGgfgcvlQm9vL2prazmRaxIPGIbB+Pg4PB5P3BqwiVDV6/XQ6/UQi8Vbyo9iMSa+CgODwYDrrrsO3/nOdxJyQS9BEaxM+QzxvW9tbUVRUVG8hxN1PB4Pu6JM6vD5Amm67enpidiNXyKRsJkJJFlUp9OxycLkZ/FaBQtkc3MTGo0GjY2N25J1Y8Gvf/1rWK1WfPnLX0ZeXh7Ky8vxhz/8IaaZEjRNY3BwEGlpaaxFZWCNO0VR6O/vZ6+vUqnc0e5yt8wI///bTxDbThzEUpSMwWAwYGFhAS0tLVt2BncqRwrWgBxMSERyjOEEzpEywOrqajgcDphMJkxMTLBWtyUlJdvuaU6nE729vThy5AjkcvmBxpuokMUgmqbj6szkX37U0NAAp9PJWk7b7Xa2/KioqCgq5Ud8FQZGoxGnT5/GN7/5TUEYcARh5yDBWV5extTUFDo7O7f1F7z66qt4+9vfHtfJc6RX7kkycE1NDcrKymJ+/GhBtsutViva29tjslLNMAysVisoimJXwXabZMYCInTb29uRn58f8+Nvbm6irq4OLpcL6+vrkMvlcLlcuOuuu/Dggw/GZAyknKqwsBB1dXV7/j6xZ6QoCm63GyUlJVAoFJBKpWF/9wMzI3ZzaYp2Kc/KygooikJzc/O270M0VvzJuQp2zvayPT3oGEhKc3Z2NmiaRmFhIRQKBbKystDX14fm5ua4OM5xAYZh2EZvLi8G+Xw+GI1Gdoc2JycHCoUCcrk8IgsvfBUGa2truPbaa/HlL38ZV199dbyHk2wIOwd8w7/x+OTJk0Gt1yQSCbxeb0LZsu0GmTi2tbVtCWZKdHw+HwYHB5Geng6VShWzh59IJEJeXh7y8vJQX1/PTjKHhobgdrvZhua8vLyYjImiKFy8eBHd3d1xEyeTk5MAwGZIuN1uiEQivPrqqzE5vtvtZuvKQy2n8rdn9Hg8WF1dxczMDCwWCzvJ3MtikxBqZgTJMdgpM4KUM3m93rAn1WKxGAsLCzCbzUGFQSi7Fnuxm+3pTmFsgX/v/1//1wh1N8L/GCkpKTh27BhKS0tZZ6qFhQUsLy+joKAAdrsdLpdrXxa+iQzDMOwOWmNjI2eFAQDW4Ugul7O7e3q9Hr29vRCJROzP9mMQwVdhsL6+juuvvx4PPPCAIAw4hiAOEhDSeJyVlbVr4jGxEuWDOCCNmXxLBna73dBoNFAqlaiuro7rWAInmXq9HpcuXYLVakVxcTHb0ByN7fK5uTksLy/jxIkTcS1vIqFzxFJULBbDbrejubk56sd2OBxQq9UHKh9JTU1FaWnplkmmTqdjMzEitZIpFov3zIwAgC984Qu49dZbUVtbu2eCNZkoT09Pw+l0oqmpaV+ftUhau+7EXiKAHCPYbkSgwxNw2SWL9BKQc7uxsYG3ve1tkEgkoCgKGo0GDMOw1zCRXchCIZGzHPxLyOrr69nE+wsXLmBzcxNFRUWsaN/rM85XYWCxWHD99dfjvvvuw7XXXhvv4QgEIIiDBMPhcECj0aCysnLPlcVYh5AFgzxo9zuhJB73JpNpxx2SRIXU1h85cgQKhSLew9lCamoqm+7r8/lgMpmwvLyMkZGRLWFBBy1/IuVUNpsNPT09cW+QLioqwic/+Uk88sgjcLvdSElJgVQqjbqtnsViQV9fX0R3xcRi8ZZMDKvVCp1Oh97eXraETKFQRFVse71ePPvss/j6178e0u/29/fj0KFDqK+v3yYivF7vtsyIQGLRKxGO+AhmWRo4hrS0tC22pGazGUNDQ1tSwHNzc9lyN/9JZrRr3OMFTdPo7+9Hbm4uGhoa4j2cA+OfeE/upxRFYWxsDNnZ2azgC9wZ4qswsNlsuOGGG3D33XfjhhtuiPdwBIIg9BwkEOE2Hvf19aGurm6LJ3iseeONN9Dd3b2vST1N0xgaGoJYLEZLS8u+Hn7nzp3DqVOnOLfqtLa2hqGhIRw/fhxSqTTewwkZhmGwvr4OnU4Hg8GAzMxMdpIZbskDabpNTU3lVC0xwzB47bXXcPbsWSgUCtx2221RbYxeW1vD8PBwxNypQoH4uFMUBZfLdaA+hd34/Oc/j+985zuQSCS46qqr8OMf/xiHDh3a9ntkMpidnY0jR47sOgb/zIjd/i9YSdNeHLRXItxeB5FIhIaGBlagGY1GjI6Ooqura8/SusAad2Kxmehp6TRNQ6vVshbGfMa/78tgMIBhGNb9yOVyYXx8nHfCwG634/Tp0/jnf/5n3HrrrfEeTrIjWJkmOktLS5ienoZKpQq5HntoaAgVFRUxdVkJ5Pz582hvbw974kjKbRQKBaqrq/c9YXn99ddx8uTJuK9I+0NKpMK5llzFZrNBp9NBr9cDANvQvNdqtMfjgVarRUlJSdDE3GSB9Fl0dXXFLdXa6/XCYDCAoihsbGyE3aewE88//zxuv/12bG5uQiQSQSKRoK6uDmNjY1u+z16vF1qtFjKZLOKfBf/dB7fbvWtJ00HLkUIh8DXKy8tZ4WkwGDAxMbGvyWCgxaa/Q1kilWGS9Ofi4uKkvC+4XC4YDAbMz8/DbDbj0KFDOHTo0IG/i1zB4XDgxhtvxD/8wz/gwx/+cLyHIyA0JCcupOzCYrGEXVbDhbIisVgc9hhsNhu0Wm1Eym3Iw5gLN1aGYTA9PQ2DwcCbEqmcnBzU1dWhrq4OTqcTFEVhZGRk19Vop9MJtVqNmpqaoKvIycL8/DwWFxfj3meRkpKyrU+BoihMTEwgKysLSqVyX30K3/ve92C329lr7/P5sLi4iJGREbS2tgK4LBJ7e3vDasAO972lpKTsKbx8Pl9Idq8H2TUIFAYFBQWsMFhZWcHU1BR6enr21XQcaLFJdoZGRkbgdDrZ72JBQQFndugC8fl8UKvVSZ3+nJ6ejszMTPh8Przzne/E5uYmKIrC+Pg4azstl8sTcifB6XTi/e9/Pz74wQ8KwiABEMQBx2EYBhkZGXtutQeDC+Ig3DEYjUaMjIxEzMqSiJN4T8RpmsbIyAhomkZPTw+v6oMJGRkZqKysRGVl5TbXHNKAl56ejoGBgaS3Zrx06RLMZjNOnDjBCeFKCNanQFHUvvoU/Etn/CfN5H8TkVhXVwelUhmdNxQixKVpr4n5TiVNwYTFbn0GGRkZbFjl4uIi5ufnceLEiYjdpzIzM9nvotfrxerqKubn5zE4OIiCggLI5fKI9AxFCq/XC7VajUOHDrHnJRkJ7DHIyspis01sNhsoioJWqwVN02z5Uazc5A6C2+3GBz7wAdxwww2444474j0cgRAQyop4zOTkJHJycuKaqDkwMICqqqqQ6upJAJhKpYrYyoharcUKf8MAACAASURBVEZzc3Ncy3dI2QTxref6jTzS0DQNk8mE2dlZ6PV6yGQytpwi3qIt1pAwJ6/Xi7a2toQSiWRniPQpyGSyXVejf/WrX+EjH/kI7HY7gMsT8JqaGkxMTLB5JXwWibvtRCiVSmRmZmJubg4rKyvo6uqKWbYJSdpeXV1FWloaK/jiVdbm8XhY+97y8vK4jIELhNN87Ha72RIyq9UasVLAaODxePCBD3wA73znO3HXXXfFezgCWxF6DpKR6elppKamRmW7PlSGh4dRVla2qwMLwzCYmJiAzWaLeACYVqtFQ0NDzBo9AyHuUtXV1SGFtvEVUjbR2dkJt9vNNjSnpaVBqVRCoVAk5FZ5OPh8PtaacT87gVwisE+hoKAACoUCMplsy+Tke9/7Hr761a9ifX0dp06dwlNPPYX8/Hz09fUlXDN+pJmamoLJZEJnZ2fcJnSkbEWv18Pr9bLlR/n5+TH5fJKysqqqqqQuMTyIK5F/KaDRaERmZiabqRAvwUfwer340Ic+hBMnTuDee++N61gEgiKIg2Rkbm4ODMPEtX5zbGwMJSUlkMlkQX9OMhuys7Nx9OjRiD+QBgYGUF1dHZe03Y2NDfT394fsLsVXpqenodfroVKptu0UkMkJRVGgaZpdxYyXmIsWHo9nS4M9n2AYhs1TMBqNW2qjSZkO8fYnLl2dnZ28u8ahQgIsyWIIV3aPSLaJXq/fV4BeuLjdbvT29qKmpiauu9vxJtJ2paT8SK/Xw+fzxVzwEXw+Hz784Q/j2LFjuP/++2N2XIGwEMRBMrK4uAiXy4Xa2tq4jWFiYoJdVQzE6XRCo9GgoqIianWmQ0NDKC8vj3missFgwPj4ODo7O1mv8mSDYRiMjY3B5XLh+PHje06CiIe7TqeDw+FIiCbKUHC5XOwkiO+ro6Q2mjhYiUQiVvDZ7XaMj4+HZNPJV8h3gpSVcfVz7b8avbq6uqsX/34g34n6+nrOZbzEkmjnGPgLvkAnsmiWsfl8Ptxxxx2oq6vDAw88ELXjCBwYQRwkIzqdDhaLJa4hMpOTk8jOzt42KdrY2IhJY+ro6CgbMhSr+va5uTksLS1BpVJF5EGaiJASmqysrH3tCJEmSp1OF1F7zVhDgu6ampp23D3jM06nE3q9HnNzc7BaraioqEBZWVnCC779wDAMhoeHIRaLOZXrsRf+zbB6vX6LF/9+UppdLhfeeuutAyWB84FYB5zRNL2l3yQjI4MVfJEsP6JpGh/72MdQVlaGBx98MGKvKxAVBHGQjBgMBhiNRjQ2NsZtDMH6HvR6PSYmJmKyqu5wODA/Pw+9Xh/1+naGYTA+Pg673Y729vaEmsRGEpJRUVpaGpGSNrKKScpWcnJyWHtNLjc0k7KyZK+tn5+fx9LSEtrb27G+vg6KorC+vr5jnwIfoWmaFcuJ3m9CdvgoioLdbmedyEJJaXY6nejt7UVjY2NSimUCF5KPbTYbex39+00OEoTIMAz+9V//FYWFhfj617+e0J/zJEEQB8mIyWTC8vIy6ykeD+bm5gAAlZWVAICZmRnodDqoVKqYe7uT+nadTgcg9MCuUPD5fOjv70dWVhYaGxuT9qbocDigVqtRX18fFXtKhmFgsVjYVcyUlBRW8MW7+c6f1dVVjI2NQaVSJVQIVaS5dOkS1tbWtjXdkj4Fsop5kKRtruPz+dDX18fLxN9wUpodDgd6e3t57VAVClwQBoF4PJ4dDQZCLT9iGAZ333030tPT8Z3vfCdpn4EJhiAOkpH19XXMzs7i+PHjcRvDwsICPB4PqqqqWAvHY8eOxb0Jz+VysUKBBHYplcp9NW25XC5oNBqUlZWxIigZISvlbW1tMevxsNvt7HX0+XyQy+VQKpX7KneIFMSZqaurizMP/1hDHMgcDkdI/SYkT4EkbZPrmOj9Ol6vl21E53uwV6Bw909pFolEUKvVaG1tjXn/F5fgojAIhAh3vV4Pg8GA9PR0VvDt1CvEMAw+85nPwOfz4bvf/a4gDBIHQRwkI1arFRcvXkRnZ2fcxrC8vAyLxYL19XUUFRVx0uefrJrodDpYrVYUFxdDqVSiqKhoz7GSNOfGxkY27TQZISvl8WzAJt7fOp0OdrudvY6FhYUx+8zNzs6yO2NcLnmKJgzDYGhoCGKxGC0tLfsS28TByuFwQCaTQalUJlyfAvHvLy8vj6uddLwgKc3Ly8swm80oLS1FZWVlwl3HSJEIwiAYm5ubbPmRx+OBTCaD1WpldwMZhsEXvvAFWCwWPProo0l5bRMYQRwkIw6HA8PDw+ju7o7bGObn5zExMYHW1taEsKsj2+Q6nQ5ra2soKCiAUqkMWhdtMpkwPDwcsTTnRGVxcRFzc3MRDa87KD6fD6urq2y5w27XMRIwDIMLFy6w9pR8r6HfCZqm0dfXh9zcXDQ0NBx4okAa00mfglQqDbvcIR4INp2Xsdls0Gg0aG1thdvtBkVRMJvN7HXkUkpzNFldXcX4+HjCCYNAPJ7Lyff33HMPtFotmpubkZeXB4lEgp/85CdxrwgQCBtBHCQjbrcbWq0WJ0+ejMvx19bW0NfXh8LCQnR0dMRlDAfB3799dXV1SyOsXq/HzMwMVCoVp2rdYwnDMFtqyrn6kA+sb8/KymKvYyT6XmiaZl1o9rNSzhdICY1cLo9KlgNJ9yXfR672KZCm22R347FYLOjr60NHRwfy8vLYf+diSnM04YswCMTn8+Hee+/F+fPnIRKJUFBQgOuuuw6nT59O6vLaBEMQB8mIz+fDm2++ibe97W0xP/by8jKmpqZQV1cHo9EY16boSEDqaXU6Hebn50HTNOrr63Ho0CFe3fBDhdgyMgyD1tbWhFkxYhhmS327WCxmG9P3471Pmk2lUiknS+ZihdvthlqtxuHDh1FeXh6TYxJ7TYqiAGCLvWa8sNvtUKvVSd90S/qPAoVBMOKd0hxN+CoMAOBb3/oWRkdH8dOf/hQSiQTz8/M4c+YMXnrpJayuruKWW27B5z73uXgPU2B3BHGQjDAMg1dffRVXXnllTI85OTkJs9mMjo4ObG5uxr0pOlLQNM3WUldXV7N1mEBknY+4jtfrZSfE9fX1Cf0AdzgcbEOzx+NhG2Hz8vL2fF+kprysrCxqIX6JAFkpb2hoiFugVWCAnkwmg0KhiGm/Cek/Svam2/X1dQwMDEClUoXdf+TvmhOLlOZowmdh8PDDD6O3txc///nPg+4Y22w2TE5Oor29PQ6jEwgDQRwkK+fOnYuZOPD5fBgcHERqaiqam5shFos50RQdCTweD7RaLWQyGWpqarZMOJxOJ7uC6XK5wppgJhrEmam8vJx3E2KSJkpR1JbG9MLCwm07I9G2bE0USMgbl1bK/ftN/Ovbo9mnQEpokr3/yGw2Y2hoKCIWvv4pzUajEVlZWRFNaY4mfBYGjzzyCM6dO4df/vKXSWu6wCMEcZCsxEocuFwuaLVaKJXKLfXGdrsdIyMjcW2KPih2ux0ajQZ1dXV7NhcGOh8Rp5VYrmBGCzIRTAZnpkD/9vz8fLaB0uFwoK+vDy0tLSgqKor3UOMGmRBzOeTNv77dYDCwfQpyuTxikzayUt7Z2RnXkqZ4s7a2huHhYXR1de2rRG83AlOaAbDlR/G0LQ4Gn4XB448/jt/97nd47rnnYp5TJBAVBHGQrMRCHFitVvT19eHo0aPbGvBcLhf6+/tx4sSJqI4hWpAH/368+8NxPuI6ZrMZg4ODnJ4IRgv/CaZOp4PT6URtbS0qKys5v4IZLdbW1tgV4kTKIvCfYNI0vSVPYT8TTJPJhJGRkaQPuzMajRgdHUV3d3dMmor9U5o3NzdRXFwcckpzNOGzMHjyySfx/PPP4/nnn0/a+x4PEcRBshJtcUD87dvb24M2nnk8HvT29uLv/u7vojaGaEFRFC5cuBCRB/9uzkdc35rV6/WYmJiIyopgIkHOQ1NTE9bX19kVzGTqNwEAg8HAToAS2V3Gf4K5n1wMg8HAfi8S+TwclHhPiMNJaY4m8T4P0eSnP/0pnnnmGbzwwgtJ/VnnIYI4SFbOnTuHU6dORWXbdX5+HgsLC7v629M0jddffx2nTp2K+PGjyczMDBtmFentU3/nI71ej7S0NCiVSigUCs49VObn57G4uIiurq6k3kYmWQ5dXV1bVs0C+00OkrSdCCwvL2NmZmbbeUh0AvsU/MvIgvUp6HQ6XLp0Cd3d3bw6D+Gi1+tx4cIF9PT0cOI87JbSHE3xzmdh8Itf/AI//vGP8eKLLyb14hBPEcRBsvLGG2+gp6cnoo14DMNgfHwcdrs9pMCnWDZFHxSGYTA2NgaXy4Vjx47FpPxnc3MTOp2OU85HDMPg4sWLsFgs6OjoSLgyqEgyNTUFo9G4Z5YDCQjS6XSwWCwoKipinVYSxep1N+bm5rCyssL79GeGYbC+vs7u8qWnp7MTzIyMDCwtLWFubg7d3d28Pg97QVEUJicn0dPTw9mFA5LSTFEUnE4n26cQyZRmPguD5557Dj/4wQ/w0ksvJVT5oEDICOIgWTl//jza29sjtqrj9XrR39+P3NxcHDlyJKQbbKKIg/28t0hDVqJ1Oh3cbndcnI+IZWtKSgqam5t5uQIeCkQEE6EYzgSfpmm21MFkMiEvL49diU60CSUJuzObzejs7Ew6oUh8+CmKgsPhAMMw6OzshFQqTdrvxsrKCqanp9Hd3c1ZYRCIf9p2pFKa+SwMXnjhBXz3u9/Fyy+/nNSN9jxHEAfJCgnkicR2oMPhgEajQWVlJSoqKkL+u0QQB06nExqNBocPHw7rvUUTYq2p0+lgs9li4nxEUm6DWbYmEzRNY2BgABkZGWhsbDzQeWAYBhsbG9DpdDAYDNtWornMQQQS35ienobBYEBpaSn0ej3bp0DyFJLl3PBh5yQSKc18FgYvvfQSvv3tb+PMmTNJbc2bBAjiIFnp6+tDXV3dnimVe0Fce1paWsL2M+e6OCBuS01NTZDJZPEeTlD8a6LX1tZQWFgIpVIZ0XAgp9MJtVqN6upqlJWVReQ1ExGv17sl0yLSkDIy4phDJiVcW50jO0ipqaloampKWqFIgh1JiR0RAYGNsHl5eVAqlQdaieY6CwsLbA9SogqDYPjvDvl8vj1TmvksDH7/+9/jK1/5Cs6cOYOCgoJ4D0cgugjiIFkZGhpCRUXFgb7kxLWns7NzX3WHXBYHe7ktcZFA56Pc3Fx2UrLfBzYRSFwKs4oHLpcLarUalZWVKC8vj8nx/EtWolETvR98Ph/6+vqQn5+f8CnYB4HsnLjdbhw7dmzH80D6FEieAjEZkMvlvHF3mZ+fx/LyMrq6ungrfoC9U5r5LAz+9Kc/4YEHHsCZM2eSOsMliRDEQbIyOjrK3tjChWEYdiu9s7Nz37Wl0XRMOggLCwuYn5/f1W2J60TC+chkMmF4eBgdHR0JI5Cigd1uh1qtjlvIG6mJ1ul02NjY2DYpiRUejwcajQZKpRJVVVUxOy7XYBgGw8PDEIvFYffe+K9E0zTNulhxLbArVGZnZ6HX66FSqZKq5yQwpVkikcDhcKCnp4d398pz587h/vvvx5kzZzi7gy4QcQRxkKxMTEygsLBwWzjZXtA0jZGREdA0jba2tgPV077++us4efIkZx4qxIlnY2MDHR0dvFoFC9f5aGVlBZcuXUp6r3aS9nvs2DFObKWTSYlOp4PRaIyZd7vb7UZvby+qqqqSurSMpmkMDg4iIyMDR48ePdCE3u12s445NpuNM4FdoTI9Pc26dXHlHh4PDAYDRkdHoVQqYTKZAHA3pTlcXn/9ddx77704c+ZM2HOFQO644w68/PLLKCkpwejo6Lafnzt3DjfccAO78HDTTTfhP/7jPw50TIF9I4iDZGVychI5OTkoLS0N+W88Hg+0Wi2Ki4tRW1t74JveX//616jkBewH8tBPTU3lvRPPXs5HMzMzoCiK99aUe0FSbvdbNhdtAr3bU1JS2N2hSAo6h8MBtVqNI0eOHHiCkMjQNA2tVgupVIr6+vqIvrbP54PJZGJT07nuYuXvUpUIQiZaBCsl4mpKc7icP38ed911F1566aWw5gk78dprryEnJwe33377juLgoYcewssvv3zgYwkcmB0nQPxZMhUIikQigdfrDfn3Nzc3odVqUVdXF5EbBRmDz+eLyGsdBLfbDa1WC7lcHpVGU66RkZGByspKVFZWss5Hk5OTsNlsEIvFSE1NRXd3d1KvBup0OkxOTnI67VckEiE/Px/5+floaGiA3W6HTqdDf38/fD7flobm/Ypdm80GrVaLlpaWpK419vl80Gg0KCkpQXV1dcRfXyKRoKSkBCUlJVtcrKampvblmBNNLl68CKvVKgiDHXoM0tPTUVFRgYqKCrY5fWVlBaOjo3FLaQ4XjUaDf/u3f8OLL74Ysef929/+dszNzUXktQTihyAOeE44E3NSe378+HFIpdK4jCFaENFTX18PpVIZ17HEg9TUVJSVlUGpVKK/vx8MwyA1NRWvvvpqVJyPEoG5uTksLy/j5MmTnH6AB5KVlYWamhrU1NSwJSsXLlyA3W6HTCZjrTVDFQobGxvo7+9He3t7UtsWejweqNVqlJWV4fDhw1E/nkgkglQqhVQqxdGjR1nRNzAwAK/XC7lcDoVCEdOME+DyThX5PHV0dPB6d3UvQm0+lkgkkMvlkMvlW3b6zp8/H7OU5nDp7+/Hxz/+cfzmN7+JeQnh+fPn0dbWhtLSUjz00ENoamqK6fEF9kYoK+I5i4uLcLlcqK2t3fX3lpaWMDMzA5VKFfFVq/7+ftTW1satgctsNmNwcJAz9eTxgjSaKhQKdlWUYRi2zIHUth/U+YjrEGtK0nPCF0FE7G51Oh3MZjMKCgqgVCohk8l2fI9cL6mKFaTXorq6GocOHYr3cOB2u1nHHKvVGrOSlVDdmZKBSLkSxSKlOVyGh4dx++234/nnn4/KDtnc3Byuu+66oGVFFosFYrEYOTk5OHv2LD71qU/h0qVLER+DQEgIPQfJysrKCqxWKxoaGoL+PBbNuZGwU90vpOFWpVJFJAguUSH15LuVi5EyB1Lbnp6ezta2RyphO94wDIORkREwDIPW1lbeTn6I3S0JecrKymKtNUnvD9lxSPZmdJLvUV9fD4VCEe/hbCNWadsMw2B0dBQ0TfP6uxEK0bIrjUZKc7iMjY3htttuw3PPPYe6urqoHGM3cRBIZWUl2+MoEHOEnoNkJSUlZceSHp/Ph8HBQaSnp6OrqytqDwOxWBzzsiKGYTAzMwO9Xp9wZSORhjjxtLW1obCwcMff8y9zOHLkCGw2GyiKgkajAQBWKHBpazwcfD4f+vv7kZubi4aGBl5PfkQiEYqKilBUVASGYWC1WkFRFN566y1IJBJkZmbCYrHg5MmTnDAKiBcOhwO9vb2cDkAUi8Xb+hQoisL09DRSU1Mj0qfgb9sqCIPo5RgQMwGlUrklpfnSpUsx6Tm5cOECbrvtNvzyl7+MmjDYC4qiIJfLIRKJoFarQdN0Uvc5cRVh54DnmEwmrKysoKWlZcu/u1wuaDQaHDp0KOpe5vPz85idnWVvitG2faNpGqOjo/D5fAe2YU10SMhbR0fHgRJ493I+4jqCd//fuHjxIpaWlpCRkQGv18tOSBLlWkaKzc1NaDQatLa27iqauYzdbmfzFPbbp8AwDJuE3djYmFSfgUDiGXBGsjH0ej28Xu+eKc3hcunSJdxyyy34+c9/HtUa/1tvvRXnzp2D0WiEXC7Hgw8+CI/HAwC488478f3vfx+PPfYYUlJSkJmZiYcffhgnT56M2ngEdkUoK0pW1tfXMTc3h2PHjrH/ZrFY0N/fH9OwJ+KWs7KyArvdzoYCSaXSiD6MvF4v+vr6WBvCZH7QLS0tYXZ2NuIhb+Ra6nQ62Gw2yGQyKJXKsJpgYwkpG6mtrY2YI0ciEqzXglxL/9p2ci35LKrJblqkzRfiSeC1LCoqYkP0drqWDMNgYGAAmZmZOHLkCCe/v7GCCIOenp64l1HuldIcLjMzM7jpppvw9NNPo7W1NQojFkhQBHGQrFitVkxOTqKjowPA5SCX8fFxtLe3x61BmNRdrqyswGKxsBOSoqKiAz2cHA4HNBoNqqqqUF5eHsERJxYMw2BqagomkwmdnZ1RrWUNbILlmvMRsehsbm5O6ppWUk/u9Xp33E0jdowURWFtbQ35+flsQzOfggLX19cxMDCAzs7OA+2mcZnAPoVg1po0TW8ps0tmuCQMAglMac7KymJ3iEIZ6/z8PG688UY8+eSTaG9vj8GIBRIIQRwkK3a7HSMjI+ju7sbs7CyWl5ehUqk4cwMkDzESCkQcVsKdXJKVwJaWlqSfBI6MjMSlpCpYqm88nY/IJDDZLTpJ8F96enrIZSP+9dAGgwGZmZls+RFX7h37YW1tDcPDw1CpVAnbOxMuwUL05HI5DAYDiouL41Z7zhW4LAwCYRiG7QXT6/VgGIYVCsHKdRcXF3HDDTfgiSeegEqlitOoBTiMIA6SFZfLBa1Wi/z8fDidThw/fpwTK7rBIA4rOp0Oq6uryMvLYyeXu61ckt2Qg9bVJzo+nw99fX3Iy8uLe8Otf8CTwWCIufMR+Uwk0yQwGD6fD1qtFoWFhQeaBJKGZoqiIBaL2Z6TRDq3pP+Gy4F3scBms0Gj0YCmaVYoRLK2PZFIJGEQDP+UZqvVimeeeQbXXnstrrnmGphMJpw+fRqPPvooenp64j1UAW4iiINkxel04pVXXkF1dXXcJ4zh4D+51Ov1yMzMRGlp6RYrRuDyluni4iKndkPigdvthlqtRnl5eUwCnMLFZrOx1xIA25weDXtZ0mvR1dWV1J8JEup16NAhVFZWRux1SXM6RVFwuVxs/xCXJ5cURbFJ2Mn8mSAJ0HK5HFVVVdtq20PpU+ALiS4MAnG73Xj++efxwgsvsOLvIx/5CO655x7e9NUIRBxBHCQjpAbf6XTi3e9+d7yHcyCsVit0Oh0oimLt4KxWK1wuF9rb2zm7GxILiOvK0aNHIZfL4z2cPQl0PlIoFBFzsZqenobBYEBnZ2dS29e6XC6o1eqoh3olwuRyeXmZFYvJbNvq9XpZsRhsAYGmaZhMJra2PVifAl/gmzDwZ3V1Fddccw0+9rGPgaIo/O53v0N2djZOnz6N06dPRyX0TCBhEcRBskHqrVtbWzEyMoIrr7wy3kOKGFarFX19fXC5XMjOzo7qKjTXIdc5UdOf/Z2PNjc3WeejcNNDGYbBxMQEHA4Hjh8/zpmJaTwg3v2xdCMDgod1kYbmeE0u5+fnsbS0hK6uLt5NcMPB6/Wit7cX5eXlqKio2PP3d+pT4MN9ls/CwGQy4dprr8XXvvY1vOtd72L/fXl5GS+//DJefPFFyGQyPPXUU/EbpACXEMRBMkFSgTs7O5GdnY1z587xRhy43W5oNBqUlpaiqqqKXYVeWVlhPdvJKjTf0ev1mJiY4E1dvb/z0fr6OtucLpPJdp3s0zSNoaEhpKSkoLm5mbOlLbHAarVCq9XuGXgXbQLLAjMyMtiG5lj5x09PT2N1dRUqlSqpdxY9Hg96e3tRWVmJsrKyfb2Gw+FgS8ncbndClJIFg8/CwGw245prrsGXvvQlvOc979nx92iaTurFE4EtCOIgGSAWluSBSFbK+CIOiC3lTuUzbrebzVJwOBzsSleiPcBCge+9Fjs5H8nl8i3N6STXorCwELW1tby7zuFAdpE6OjriZlO8E5ubm2xZIAD2u5mTkxOV4/nnOSTzRMjtdqO3txc1NTURy/gI5sFPrKi5LML4LAw2NjZw7bXX4vOf/zyuu+66eA9HIHEQxAHfIaunYrEYLS0tWx6IfBAHa2trGBoaCtmW0uv1wmAwQKfTwWKxcD6oK1QYhsHFixdhsVjYICu+s5PzUWFhIYaGhlBRURFSqQSfMRqNGB0dTYhdJJfLxa5COxwONgk23FKyYJDyMqfTiWPHjiW9MHjrrbdQV1cHpVIZlWME9ink5OSwfQpc6u/gszCwWq249tpr8elPfxo33nhjvIcjkFgI4oDPuN1uaLValJSUoKamZtsD9ty5czh16lTCToqXl5cxPT0NlUq1LwtCEu4ULKgrkSYPNE1jeHiYFYCJej0Pis1mw8LCAmZmZpCVlYXDhw/zohZ6v1AUhYsXL6K7uztmJTuRgoh4iqKwsbFxoCRYkvEBIKm/H8BlAfbWW2/hyJEjMTMpYBiGNY4wGAwQi8VsKVk8BSufhYHNZsPp06fxiU98Arfccku8hyOQeAjigK+QUpuGhoYdV4feeOMN9PT0JFzKKSmTMhqNEXOfCSxXycvLQ2lpKedTYL1eL7RaLYqKipK+fIY0pLe2tiIrK4stV/F4PGy5SiScjxKBxcVFzM/P88KJJ1gpWahuOSToLSMjA0ePHk2Ka78TTqcTvb29OHr0aEwb0gNxOBys2QDpU1AoFJBKpTG7PnwWBna7Hddffz3uuOMOfOhDH4r3cAQSE0Ec8BGTyYTh4WEcP358Vx/j8+fPo729PaFujmSVXCQSbSuTihQMw2B9fZ1d6crKymKzFLjkbOJ0OqHRaFBVVbXvhkK+QBJu29vbt9XVR8r5KFEgtq0qlYrTwnY/ELcc8t0k9sUKhWLb7iFN0+jr60N+fj7q6+vjNGJuQJyqmpubOZUU7/F4WLMB0qew3x2iUOGzMHA4HLjxxhtx22234fbbb4/3cAQSF0Ec8I2FhQXMzc2FVGqjVqvR3NycMGUXHo8HWq0WxcXFMVsl998SpygKaWlpKC0tjVmi706QnaGmpibIZLK4jYMLkPKZrq6uPT/zgc5HiVpKFgzSd2K1WpOm4dZut7PfTZ/Px5arZGVlQavVQiaToaamJt7DjCt2ux1qtRotLS0oKiqK93B2hOwQkT6F7OzsiPcp8FkYOJ1O3HTTTXj/+9+Pf/qnf4r3cAQSG0Ec8AWGYXDheIoSsQAAIABJREFUwgW2ITWUFcO+vj7U1dVxzsEkGA6HA2q1GrW1tVENb9oLf3cVkUjEZinsp+dhv4TbhM1nFhYWsLCwsK/ymWClZGQykmgr7qSunqZptLW18XJHZC+IK9ny8jKMRiMKCwvR0NCQ8GYDB4EEIba1tSVU3glZlCF5CpHoU+CzMHC73bj55ptxzTXX4M4774z3cAQSH0Ec8AGfz4f+/n5kZWWhsbEx5Afh4OAgDh8+zPmHBrFijLdHeyDE41un07GrltG0YQQAnU6HycnJkFbJ+QzpO1lbWwtZDO/1esGcj+K9QxQKNE1jYGAAmZmZSV9X73a7oVarUVFRgbS0tC1mAwqFAjKZLCmcvIDLu4sajWbP8tJEgOTWUBQFl8vFlgaG2qfAZ2Hg8XjwwQ9+EFdddRU++clPxns4AvxAEAeJDsMwePPNN1FWVobDhw+H9bcjIyNsSQVXIYFenZ2dUZ10HxS3280KBafTyTbA5uXlRWyyNjs7i5WVlaRPdWUYBqOjo/B6vWhra4tK+YzNZmN3iMiqJRedj3w+35aG9GTG5XKht7cX9fX1UCgU7L8zDMOWq6yuriIrK4vNxkj0Zu2dIKF3fNxdDHSyIqGIO/Up8FkYeL1efOhDH0JPTw8+/elPx3s4AvxBEAd8wOl07suqcHx8HEVFRTGztAsXMhlWqVQJ9RAnYUA6nQ5Wq5VNDd1vAyzDMBgfH4fD4cDx48eTZuUzGDRNs7tksVol998h8nq9nHE+8ng8UKvV+1oY4Buk4XavHhz/HiK9Xg+JRMLuEHFN+O0Xi8WCvr4+TobeRRqapmE2m9nSwKysLLY0MD09ndfCwOfz4fbbb0drays+97nPxXs4AvxCEAfJzMWLF5GbmxuxhMxIwafJcLAG2NLSUhQVFYW04k1KRjIyMsIqGeMjpCGd5HbEawxEKNjt9rg5H5FV8traWs59f2MNqavfT8Otv/DzeDxsXXskd/xiCSnBVKlUnN5pjQYMw7A7fnq9Hl6vF263GyqVilPlqJGApml89KMfRV1dHR544IF4D0eAfwjiIJmZnp5GWloaysvL4z0UFp/Ph76+PuTm5uLIkSMJ+YDeCZIaqtPpYDKZkJ+fz2YpBBNAHo8HGo0Gcrk86R1XXC4X1Go1p2xbfT4fu0NEgrpi4XxE3GcaGxvj6lfPBUj5TCTq6v0tb202G4qLi9nE7URwfjKbzRgaGkqINOxos7q6itHRUZSXl8NkMkU8cTue0DSNj3/84ygtLcVXvvKVA7/eHXfcgZdffhklJSUYHR3d9nOGYfCpT30KZ8+eRVZWFp566im0t7cf+LgCnEYQB8nM3NwcAKCysjKu4yC4XC5oNBqUl5fzvkyCYRh2O9xgMCAnJwelpaUoKSlBamoq685UV1cnrAz//5VhLk+GgzkfKZVKlJSURNT5iEyGudacHw82NjbQ398flfIZkp5OURRMJhOkUimUSiVnQxFJzkdXVxdvyqP2S7BSIq/Xi9XVVVAUhfX1dRQUFCRkgzrDMPjEJz4BqVSKb3zjGxEROa+99hpycnJw++23BxUHZ8+exSOPPIKzZ8+it7cXn/rUp9Db23vg4wpwGkEcJDOLi4twu92cWJUm6bZcngBGC/9gJ1IHvbm5iba2ti2NlckImQAmkuOKv/ORXq9HZmYmW65ykLpns9mMwcHBpKgl3wsyGY7FKjkR8hRFwWAwROx6Rgqj0YjR0VF0d3cntYMZEFrzcWCDemZmJtugzoXruRNkBT81NRUPPfRQRHc/5ubmcN111wUVB//yL/+CK6+8ErfeeisAoKGhAefOnYNSqYzY8QU4x44fLu4tjQhEHIlEAq/XG+9hwGg0YmRkJGknPSKRCPn5+cjPz0dxcTGGhoZw6NAhXLp0CdPT03HJUuACZNKTaPXTIpEIUqkUUqkUR48eZeug1Wr1vp2PVldXMTY2hu7ubmFl2O9cxOI7IRKJUFhYiMLCQjQ2NrL++2q1ms06OYj//kHwnwzvx5SCT4TafCwSiVBUVMT2p5DrqdFoAIAVfly65zAMg89+9rMAEHFhsBfLy8tbSo/LysqwvLwsiIMkRRAHSYBEIoHP54vrGBYXFzE7O4sTJ04k/cNteXkZ09PTuOKKK9hz4XA4oNPp0N/fD5qmWaHA95rilZUVTE1N8WLSk5OTg7q6OtTV1bENsIODgyE7H+l0Oly6dIkX5+KgkDTseJ6L3Nxc5Obmoq6ujvXfHx4ehtvtZp3J8vPzoz6BMxgMmJiYQHd3d9J/Lg7iSuR/PV0uFyiKwtjYGBwOR9wMB/xhGAZf/OIXYbfb8YMf/CDm4whWRZLIPRsCB0MQB0lASkpK3MQBwzCYnJzE+vo6Tp48yck63ljBMAymp6exurqKEydObMkwyMzMRHV1Naqrq9kH18jICFwuF7sCHW9LzUgzOzsLnU637VzwgczMTFRVVaGqqopN9L1w4cKOzkckAZqP5yJclpeXMTMzgxMnTnDG2jgjIwOVlZWorKxkLYynp6dhsVhQVFQEpVIZsjNZOFAUhcnJSV5adIZLJO1K09PTcfjwYRw+fJjtU5ifn8fQ0BCkUinbpxDL59WXvvQlrK6u4oc//GFc7vNlZWVYXFxk//+lpaWk74NLZoSegyRgfX0dc3NzOHbsWEyPS9M0BgcHkZKSgpaWFl5NbMOFBHp5PB4cO3Ys5EmEv7PK5uYmZDIZSktLQ04M5SIMw+DixYuwWq1ob29PqEbBgxLM+YhhGDgcDqhUqqQWz8BlkbS4uJgwAYA0TW9paI5kg/rKygqmp6fR3d3NGZEUL2KVY+BvIEH6FGLRd/LVr34VU1NT+MlPfhJVx6zdeg7OnDmD73//+2xD8t133w21Wh21sQhwAqEhOZlxOBz461//irKyMpSWlsZkBdrfnrO6ujphJ7KRwOfzob+/H7m5uWhoaNj3uQicWBYVFaG0tDRhLBiByw/f4eFhiESipBeMPp8Pg4ODMJvNEIvFyM/Pj4rzUaIwMzMDg8GAzs7OhHz/DMNgfX2dbWhOT09nJ5bhlgMtLy9jdnYW3d3dCSGSokk8A85sNhsoigJFUQAAuVwOhUKB3NzciB3j29/+NoaHh/H0009HdaHk1ltvxblz52A0GiGXy/Hggw/C4/EAAO68804wDIO77roLv//975GVlYWf/OQn6OzsjNp4BDiBIA6SHbIVvrKygs3NTbZmNhor0Ha7HRqNRrDnBOB2u6HRaHDo0KGIWsmSFUudToe1tTVIpVKUlpaiuLiYsyvxJNsiPz8f9fX1SS0MiEgCgNbWVgCXd/iI5S3XnHKiDSk97Ojo4OznN1z8J5YMw7DlgXs1wC4uLmJhYSFhdk+iCZeSj10uF7uLS/oUFAoFCgsL930ve/jhh/HWW2/hF7/4RUIKYoGERxAHAn/D6/WyK9AWi4UtVYlEMxaxYTx27BgKCgoiNOLEhIRYHTlyJKpWpcSyj2yFkzRsLq1AezweqNXqiIukRISmafT39yM7O3vHAEDirEJR1L6djxIBhmEwMTHBpqQnyg5YuJA+Ioqidg3qmp+fx/LyMrq6ujjz3Y0XXBIGgfh8PjZPwWw276tP4ZFHHsFf/vIXPPvss0kvAgXihiAOBIJDbnI6nQ7r6+tsqUpRUVHYQkGn02FychKdnZ28d9nZi/X1dQwMDMRcJAXz3icWjPGqWyZBb/X19Ulvi+f1eqHVaiGTyULOHSHORzqdLmTno0SA9OHQNI3W1taEfi/hQBZnKIrakrhttVphMBjQ1dXFm92T/cJlYRDITvkYcrl8x3Kyxx9/HGfPnsWvfvWrpO8nEYgrgjgQ2JvAUpWCggK2VGWvFb3p6Wno9Xp0dnYm/c3OYDBgfHw8JsFNe2G1WqHT6UBRFFJSUlBaWrqvGuj9YrPZoNVq0dLSwvqNJytk96S8vBwVFRX7eg3ifKTT6XZ0PkoEGIbB4OAg0tLS0NjYmFBjjyQkcfvChQvY2Nhgyz3lcnnSriYnkjAIBikn0+v1YBgGi4uLqKurQ3t7O8RiMZ588kn8+te/xgsvvJCQ70+AVwjiQCA8GIaByWSCTqeD0WhEfn4+SktLt8XQ79eFh68QS0qVSsW5G7/dbodOp4NOpwMANkshWqUqQtLv33A6nVCr1airq4vY7gmxYPR3PlIqlSGJ+XhCyqpyc3OTvvcEAKamprC2toaOjg42SE+v1yMtLY3tO0mWYMREFwaBuFwu/OIXv8DTTz+NpaUlNDQ0wGAw4JVXXuFU+JpA0iKIA4H942/vZjAY2Jr2wsJC1hc62R/y/nkOHR0dnK8XJqFOOp0OHo8HcrmcdbKKBGT3pKuri3d18uFCek+ampogk8micgyaplkxH2lLzUji8/mg1WpRXFwcclkVn/G39A0UdETMUxQFmqa3OOXw8V7LN2EQyFNPPYUnn3wSdXV10Gg06OjowA033IB3v/vdcd9hFkhaBHEgEBlITfvi4iLm5+eRm5uLmpqapN4Gp2l6iz0nl1dtg+HxeFihYLfbUVJSgtLS0n2nvy4uLmJubg5dXV28fMiHg8ViQV9fX0x7T4ilpr/zUbz7ToDLOx1qtRqlpaVJ35ROsj42NzdDasR2u91sQzMpJzuoUw6X4LsweO655/CDH/wAL730EnJyckDTNDQaDX7729/ij3/8IxQKBR5//HGUlZXFe6gCyYUgDgQih8ViQX9/P5qampCens6ubqWnp7M17cnSd+D1etHX14eCggLU1dUl/IM60MmquLiY3SUK5b2RBOhE9aqPJKSsqrOzM6K+6OFC+k70ej3EYjFbThbLUhWPx4Pe3l5UVlYm/QSIODS5XC4cO3Ys7HuGv4mE2WxGYWEh65STiI3MfBcGv/nNb/Dwww/jzJkzO94HpqamUF5ezsv3L8BpBHEgEBlIuUhHR8e2G53NZsPKygooikJqaio7CeHrDc/lckGtVqOyshLl5eXxHk7EoWl6yyRktwZ1hmEwPj4Op9PJa0vKUOFqWVU8nI9cLhd6e3sj2m+RqDAMg7GxMfh8vog4NAXaGGdnZ7MNzYmwQMN3YfDyyy/jW9/6Fs6cOYP8/Px4D0dAIBBBHAgcnPn5eTacZ68bud1uZ4WCSCSKy2plNCEuPI2NjSgpKYn3cKJOYIO6f027WCzG4OAg0tPTk9p5hrCysoKpqSl0d3dzesITC+cjYmN79OjRpPie7AbDMBgZGYFIJEJzc3PEvycMw2zZJZJIJGw5GZcEKoHvwuD3v/89vvKVr+DMmTNJn/kjwFkEcSCwfxiGwYULF9jGuXDLRRwOB+uSQ9M0lEolSktLOfnACoW1tTUMDQ2hvb09KVeD/Gva9Xo9XC4XiouL0dbWlrR9J4T5+XksLS0lXLptNJyPSCO2YGN7+TszNDSE1NTUmAnoYLtECoUCeXl5cRfwfBcGf/rTn/Dv//7vOHv2bNJ/9gU4jSAO+MCrr76Kxx9/HDfffDPe+973xmRy7fP52FXhpqamAz9UXC4XKxQ8Hg8UCgVKS0sTxtaNBL2pVKqEFTeRwu12o7e3F3K5HAzDQK/XIzU1le074eNDfzempqZgMpnQ2dmZkLXfhEg4H1mtVmi1Whw/fhxSqTTKI+Y2DMNgYGAAmZmZOyZiRxuPx8PuEtlsti0NzbEuAeS7MDh37hzuu+8+nDlzJul3ywQ4jyAO+AB5yPz617/G2bNnUVtbi5tvvhnXXHNNVBoe3W43NBoNlEolqquro/L6ZGXL6XRusdOM98pWMGZnZ7GysgKVSpUQ9bzRhKwKHz16FHK5nP33zc1NtkFdJBKx4o8v5WTBIA2mDoeDd/0W+3E+2tjYQH9/v5BvgctCa2BgADk5OWhoaIj3cABcXvDxD7uUSqVQKpWQyWRRNxHguzB44403cM899+Dll1+GQqGI93AEBPZCEAd8g4SP/epXv8KZM2dQVlaGm/8fe3ceF9V99Q/8IyhurMM6V1xRlIiCykCk0Zgo0YgIODeNMY3JY+1j0sTGn01ajYkxTX1laZbnSczSLI2JbdzugCASiZpoH42yGIyKKyoq3Blm2Hdmu78/krkVRGWZmTvLef+lcJk5MCzfc7/new7LIiUlxSqlLs3NzSgsLMSECRPs8kvOcmeL53mrtNO0Jsvir7m5GVOnTnXqu8LWYGnPGRMTA5lMdsvr2traxF0io9HodLtE3SEIQoc2tlJ/r9ranTof1dTU4OTJk4iLi3Op17k3zGYzjh8/Dn9/f4wbN07qcLp04wwbnU4nJn+hoaFWX7y7emJw9OhRPPPMM9i9ezcYhpE6HEK6g5IDV3f27FmoVCpkZ2cjJCQESqUSqampt1283Yqlpl6qkgBLO02e59HY2IiQkBCrH5TsLrPZjBMnTsDLy8sqZVXOrrq6GqdOneqyW9Xt3LhL1NraKu4SOUL9c29ZFn8+Pj4YP368034evWU5S6TRaGA0GuHj44OamhpMnz7d7UvunHXYW2NjozhPwcPDQ5zQ3NchXa6eGBQWFmLFihXIyspyyc51xGVRcuBOSktLoVKpkJWVBR8fH7Asi7S0tG5NZ+V5HhcvXkR8fLxDlIJYenrzPI/6+noEBgaCYRgEBgbafDFmMBhQVFSEkJAQp/oDbyuW8xZ9/d4wGo1i/XNjYyOCg4PBMIwkyV9vGY1GFBYWIjQ01CYld86moqICZ86cgbe3N9rb28WE3t/f32leU2sxmUwoLCxESEiIU39v3DhFXa/Xi69pT3dzXT0xKC4uxrJly5CZmen2w/2I06HkwF2VlZVBpVJh165d8PLyglKpRHp6+k39xs1mM7Zu3YoxY8YgLi7OITutmM1mVFVVged5cfhPXzuq3EpraysKCwsRERGBYcOGWfWxnZGtuvDcONCprq7Opq+ptej1ehQUFGDkyJF0lxA/31C4dOkSEhIS4OXlZZPOR87CkjTK5XKXWigaDAZotVpoNBo0NDQgMDAQcrkcgYGBt31NXT0xOHnyJJYuXYqMjAynTgSJ26LkgADl5eXIyMhARkYGACA9PR2LFi1CaGgofvOb38BoNGLHjh1OMdnW0nef53lUV1d3OFTX1zMBlgnQ1ILx56/zhQsXUFdXZ/MuPJ275Pj5+YldchzlnEdbWxvy8/Mxfvx4OnAI4Nq1a7h+/fotk0ZrdD5yFkajEfn5+Rg+fDhGjBghdTg2Y7lJYznQfKvXVKvV4uzZsy6bGJSUlODRRx/Fzp07HfZMCSF3QMkB6Uij0SAzMxPbt2/H5cuXoVAo8Le//c0p735YDtXxPA+dTtenBYilpn7q1Klu32nFMrTJbDZj8uTJdr3r2/mg5NChQ8EwDEJCQiTb1bIc0o+OjkZQUJAkMTiSK1euQKPRQKFQdOvnrDedj5yFwWBAfn4+Ro0ahfDwcKnDsRvLa6rRaKDVajFw4EDI5XJ4enri0qVLLpsYnDt3DosXL8a2bdswYcIEqcMhpLcoOSA3q6iogFKpxG9/+1sAgEqlQn19PVJTU6FUKp3yboggCKivrwfP89BqtRg6dKjYfeNOi8qKigpcunQJCoXCIc5bSMlkMuHHH3+Et7e3ZL3ZLSyTX3meR2VlpbgAsecsBUuHJurb/7OLFy+itrYW06ZN6/Wuzp06HzkLg8GAY8eOISIiwu271DQ1NaG0tBTl5eXiTRq5XO5SnasuXryIhx56CP/6178wceLEPj/e3r178eyzz8JkMmH58uVYs2ZNh/dv3rwZzz//vFje+swzz2D58uV9fl5CQMkB6eynn37C448/jk2bNuGee+4R315TU4Ps7GxwHAetVouUlBSwLIuoqCgJo+2dzovKQYMG3fJO5aVLl6DVah32vIU9GQwGsW569OjRUodzk6amJrFLjj0WldSe8z8s09JbWlqsOtPhxinqJpMJYWFhkMvlNpnfYk16vR7Hjh3DuHHjbjrH5Y5uLCUCIHY+am1tdYlD6pcvX4ZSqcTmzZsRExPT58czmUyIjIzEvn37EB4eDoVCga1bt+Kuu+4Sr9m8eTOKioqwadOmPj8fIZ1QckD+Y//+/fjTn/6E7du333Z3oL6+Hrt374ZKpcK1a9ewYMECsCyL6Ohop/zlbrlTqdFoxEm+oaGhKC0thV6vR2xsrMsfmLyTtrY2FBQUYOzYsU5xF/TGRaXZbBYXldZaxFsWO47SvUtKltkqljIzW/0O6Nz21lEXle3t7eL5kxsHAbqr250xsLSn1mg0TntI/erVq0hLS8Pnn3+OqVOnWuUxjx49ig0bNiAvLw8A8NprrwEA1q5dK15DyQGxIUoOyH+UlJQgNDS0R3XTjY2NyM3NhUqlwsWLF/Hggw+CZVlMmTLFof5gd1dzc7NYRuTp6YmxY8c6ZUmDNVlq6idOnNittreOpr29XVxUtre393nidkVFBS5fvoz4+HiXrJvuCUEQ8NNPP6F///52nfdhWVSq1eoedcmxNcvB9KioKISEhEgWh6PoyeFjyyF1jUaDqqoq+Pj4ICwsrFuln1IpLy/HwoUL8fe//x0KhcJqj8txHPbu3YvPPvsMALBlyxbk5+d3SAQ2b96MtWvXIjg4GJGRkXj33XepSxqxFkoOiPW0tLRg79694DgOZ86cQVJSEliWRXx8vNMkCnq9HoWFhRg2bBhCQ0PFu8+CIIhlKu40yKmurg7FxcUuU1NvmbitVqvR3NyM4ODgHg3SKysrQ0VFhdVbtzojs9ksnj+RctibpUuORqPp0M0qODjYrp2PWltbkZ+fTwfTf9GXrkSCIKChoUE8e+Ll5SUOXnOUGzU8zyMlJQWbNm3C9OnTrfrYO3fuRF5eXofkoKCgAO+//754TXV1Nby9vTFw4EB8/PHH2LFjB7777jurxkHcFiUHxDba2trw7bffQqVSobi4GLNnz4ZSqURiYqLDbhe3tLSgsLCwy3aUlsE/PM/DaDS65IG6znQ6HUpKSqBQKPo8CdURmUwm8e6zZZDe7e4+X7x4ETU1NTZv3eoMLJN+AwMDMXbsWKnDEUnV+ailpQUFBQXU5vgX1m5X2tLSIpZ+ms1mhIaGir9/pUhKKysrkZycjHfffRczZsyw+uN3p6zoRiaTCTKZDPX19VaPhbglSg6I7en1ehw4cAAcx6GwsBAzZ84Ey7KYMWOGwyyy6uvr8eOPPyImJgYymey21+r1enFHob29Xaxnd6UWp5bSqvj4eAwaNEjqcGyuc4/2G+djeHh44MyZM2hvb6fzJ/i5pKegoAAMwzj8QK8bzxP1799f/Fm15t1nS9nd5MmT7/i7wx3Yeo6B5eyJRqNBS0tLj3f/+kqn0yE5ORlvvvkmZs2aZZPnMBqNiIyMxIEDBzBs2DAoFAp8/fXXHbogqdVq8bB7ZmYm3njjDRw7dswm8RC3Q8kBsS+DwYBDhw6B4zgcOXIEv/rVr6BUKjFr1izJyjS0Wi3OnDnTq64zBoNBrGdvaWkR69l9fX2dppSqs8uXL4t96t2xdKbzfAyj0Qhvb2/qWIX/9O13xinQnQ+pW+4+96XzUVNTEwoLC12m7K6v7D3g7MZJ6rW1tZDJZAgLC7PK0MuuVFdXY/78+di4cSPmzJlj9ce/UW5uLlatWgWTyYRly5Zh3bp1WL9+PeLi4rBw4UKsXbsW2dnZ6N+/P2QyGT766COarUCshZIDIh2TyYTDhw+D4zgcOnQICoUCLMti9uzZdht+dP36dZSVlVnlcKnlkCTP82hqarL7Ha2+srSjbG5uxtSpU93+DrmldGbQoEHw8vJCZWWlSw3o6qn29nYUFBS4RN9+a3Q+amxsRFFREaZOnQo/Pz8bR+z4pJ58LAgCampqxAGJ3t7e4oFma/ys1tbWIjk5GevXr8e8efOsEDEhDouSA+IYzGYzjh49Co7jcODAAcTGxoJlWTzwwAM2KWsRBKHDwCZrH1zsXM8eFBQEhmEgk8kcMlEwm81i1xlnbUlrTZbSmc4zHTqXqVjOnrh66ZUrd+HpTecjy/C7adOmuVQ5YW9JnRh0ZpllYznQ3NeSsvr6eiQnJ+PPf/4zUlJSbBAxIQ6FkgPieARBQGFhITiOw7fffouoqCiwLIsHH3zQKp2CBEHAyZMnIQgCJk+ebPM75Gaz+aatb4ZhJG+7aGG5Qx4QEIBx48a5fWKg1+uRn5+P0aNHIzw8/JbX3XhIUhAEcfHhaoe3LYdt3aELT+ezJ111PrKcT4qLi3P4YWz24GiJQVcsJWUajQZGo7FDSdmdft81NjYiOTkZ/+///T+kp6fbKWJCJEXJAXFsgiDgxIkT4DgO33zzDSIiIsCyLObPn9+rP8xGoxHHjx+Hv78/IiMj7b4QtvTy5nlePPjKMIx48NXeLK1bw8PDMXLkSLs/v6NpbW1FQUEBJkyY0KMBVpZuVmq1GgaDoUeLD0fW1NSEoqIixMTEICAgQOpw7Mpy9sRSpjJkyBD4+vqC53nEx8e7dKey7nKGxKCzG9sZW8o/w8LCIJPJbvod3NzcjAULFuCpp57Cr3/9a4kiJsTuKDkgzsMyiZXjOOzZswfh4eFgWRYpKSndqvm11EyPHDkSI0aMsEPEt9e5RtbX1xcMwyAkJMQuXZwsC+GuWre6I8tCuK/tKDsfUnfUSb53QqUz/yEIAsrLy1FSUiKeQbGcPXGUvvv25oyJQWcmk6nDTtG2bdswffp0KJVK9O/fHwsXLsSyZcuwZMkSqUMlxJ4oOSDO6+zZs1CpVMjOzkZISAiUSiVSU1O7bCd47tw5lJeXY/LkyQ5ZM23pz27pkDN06FAwDIPQ0FCbDHKyHKbsTutWd2ApFbH24dLO9exBQUFiPbsjJwq1tbU4ceIEFAoF3SHHz11qTp06hYSEBAwePNgmnY+ciSskBp0JgoBvv/0WO3fuxKFDhwAA9957L15//XWXL6cjpBNKDohrKC0thUqlQlZWFnx8fMCyLNLS0hAcHIz9+/fjySefxM6TkSbnAAAgAElEQVSdOzFlyhSpQ70jy3RQnufFDjkMwyAsLMwqrTRramrw008/0R3hX1gWfr1pZdsTlnp2nudRW1uLgICADrMUHEVVVRVOnz6N+Ph4t5oGfiuWYYCWxKAza3Q+ciaumBjcqL29HYsWLcLdd9+NAQMGICcnBwMGDEBqaipSU1M7NCggxEVRckBcT1lZGVQqFXbt2oW2tjbU1tZi8+bNuOeee6QOrVcaGxvFRGHAgAFiotCbP8yVlZU4d+4c4uPj3bYc4kZSfT0sJWU8z6Oqqgq+vr6Qy+UICQmxyU5Rd1kWfgkJCS7fgak7evr16E3nI2fi6omBXq/HQw89hHnz5uGpp54S365Wq5GdnY2srCzU1NTg0KFDLvn5E/ILSg7c0c6dO7FhwwacPXsWBQUFiIuL6/K6UaNGwcfHB56enujfvz+KiorsHGnffPrpp/jiiy+QkpIijqFPT0/HokWLnG6Ak0VzczN4nodGo4Gnp2ePWmleu3YN165dQ3x8vNv16O9KeXk5rly5goSEBEm/HoIgoL6+HjzPQ6vVYsiQIWI9uz2HrvE8j9LSUiQkJNDCB4BGo8GFCxd6/fW4Vecje50psjZXTwwMBgMWL16MWbNmYeXKlbe8rqWlhXbUiKuj5MAdnT17Fh4eHlixYgXeeuut2yYHRUVFTldvKQgCXn75ZZw9exZbtmwRF84ajQaZmZlQqVRoa2tDeno6lEolRo0aJW3AvdTa2iomCoIgQC6Xg2GYm+6AC4KA0tJSVFdXIy4uTtI7047iypUrUKvVDjkFuvNOkSUBtOWC7Pr162Li6GhfDymo1WoxUbJG4thV5yO5XG61AV225uqJgdFoxKOPPoqEhASsXr1a6nAIkRolB+5s1qxZLpccGAwG/O53v4O/vz/eeeedW27l63Q6ZGVlgeM41NfXIzU1FUqlEuPGjbNzxNbR1tYmHpA0mUwICwsDwzAYMmQISkpKoNfrERsb6xKlDX0hCAIuXLiA+vp6TJs2zeHv4DY3N4v92fv16yfOUrDmncuysjIxUaLEEaioqBB3lGyRKHU1oMuROx+5emJgMpmwdOlSTJo0CWvWrJE6HEIcASUH7uxOycHo0aMREBCAfv36YcWKFfjv//5vO0fYczU1NcjIyMDy5ct79DHZ2dngOA46nQ4LFiwAy7KIioqyYaS2097eDo1GIx589fX1xeTJk93+8LEgCCgpKYHBYEBMTIzTJUo3JoBGo1FMFPrSIefGHSVHT5TsQYodlBuH6ZnNZvF1dYQuUa6eGJjNZixbtgwRERF46aWXpA6HEEdByYGrmjNnDjQazU1v37hxI1JTUwHcOTngeR4Mw0Cr1SIpKQnvv/8+Zs6cadO4pVZfX4+cnBxwHIdr166JiUJ0dLRTdR4xGo0oLCxEYGAgBg8eDJ7n0draitDQUDAMA19fX6f6fPrKbDbjxIkTGDhwIO666y6n/9w7d8ixtNL08/Pr1ucmCALOnz+PpqYmTJ061ekSJVu4evUqKioqEB8fL9kOSnt7uzigy/K6hoWFSdL5yB0SgxUrViAsLAyvvvqq1OEQ4kgoOXBnd0oObrRhwwZ4e3vjueees0NkjqGxsRG5ublQqVQoLS3FvHnzwLIspkyZ4tCLS8uwt9GjRyM8PFx8u9FoRGVlJXieR3NzM4KDg8EwjMu2XLQwmUwoKipCQEAAxo0b53Kfq6VDDs/zaGxsRHBwMORyOWQyWZefq2UHxWg0IiYmxuW+Hr3hiKVVUnY+cvXEQBAEPP300/D19cVrr71GPwOEdETJgTu7XXLQ3NwMs9kMHx8fNDc3IykpCevXr8e8efMkiFR6LS0t2Lt3LziOw5kzZ5CUlASWZREfH+9Qf1haWlpQUFCAu+6667bD3kwmk7igtAznYhjmlgtKZ2UwGFBYWAiGYZz24HlPWCa+8jyPuro6yGQyyOVyBAUFwcPDA4Ig4OTJk/D09MTEiRNd6rXurcuXL0On0zl0aZU9Ox+5Q2KwatUqeHp64u2336afAUJuRsmBO8rMzMTKlSuh0+ng7++P2NhY5OXlged5LF++HLm5ubh8+TLS09MB/HwHa8mSJVi3bp3EkTuGtrY27Nu3DxzHobi4GLNnz4ZSqURiYqKk5RmWKb+xsbEICAjo9seZzWbodLoOC0qGYZy+N7tlB2XMmDEYNmyY1OHYndlsFmcpVFdXw9fXF62trZDJZIiKiqJFEX4+c1FTU4O4uDin+V6/Vecja7S+dYfE4Pnnn0d7ezvee+89+hkgpGuUHBDSF3q9HgcOHIBKpUJBQQFmzpwJlmUxY8YMu96FtEy17euUX7PZjOrqavA8j5qaGoed4nsnra2tyM/Pv+MOirswGo04duyY+O+hQ4eKrTTdtXXpjV2rnOl7+0bW7HzkDonBCy+8gNraWnz00UeUGBBya5QcEGItBoMBhw4dAsdx+OGHH5CYmAilUolZs2bZdAFmGV4VHx9v1am2XU3xZRjG4Yc4NTU1obCwEDExMZDJZFKHIznL4fSwsDCMHj1aXFBaZikMHDhQXFC64qKwM8th7ObmZkyZMsVpE4Ou9LbzkasnBgDw8ssvo7y8HJ9++qlLveaE2AAlB4TYgslkwuHDh8FxHA4dOgSFQgGlUok5c+ZYdehRWVmZ2GHFlgnIjaUMWq0WPj4+YqLgKAc4AaCurg7FxcWYOnUq/Pz8pA5HcgaDAQUFBRg+fDhGjBjR5TVNTU3igtLDw0McuuaIPff7ShAEnD17Fu3t7YiNjXXpu8eWlsYajea2Ha3cITH461//igsXLuCLL75w6BsbhDgISg4IsTWz2YyjR49CpVLhwIEDiImJAcuyeOCBB3p9p1/KYV6CIKChoUG882zNmue+sJRWKRQKDB06VLI4HIVer0d+fj4iIiLAMEy3Pqa1tVWcpeBoPff7ytKlyWQyYfLkyS6dGHTWufNRUFAQ5HI5TCYTzp0759KJwZtvvokTJ05gy5YtlBgQ0j2UHBBiT4IgoLCwEBzH4dtvv0VUVBRYlsWDDz7Y7am3lo4zABxikdPQ0CDeebaUqMjlcqvukNyJRqPB+fPnER8f75J3vHuqra0N+fn5mDBhAkJDQ3v1GJY7z2q1Gu3t7eKdZ2eckSEIAk6dOgUAmDRpktPFb02WzkeWLk1yuRzh4eEIDg52ucXzu+++i6NHj+Lrr7+2yg7n3r178eyzz8JkMmH58uU3TVRub2/H0qVLcfz4cQQGBmL79u1u0SWNuBxKDgiRiiAIOHHiBDiOwzfffIOIiAiwLIv58+ffcuqt0WjEjz/+CD8/P0RGRjrcIufGEhVPT08wDIOwsDCrnoXo7Pr167h69Sri4+PtmpA4Kks72+joaAQFBVnlMQ0Gg9j61jIjQy6XixPUHZkgCPjpp58wYMAAlxiAZw2WUqKEhATxnIK1Ox9JbdOmTThw4AB27Nhhlc/FZDIhMjIS+/btQ3h4OBQKBbZu3Yq77rpLvObDDz/EyZMn8fHHH2Pbtm3IzMzE9u3b+/zchNgZJQeEOAJLyQPHccjJyUF4eDhYlkVKSopYO19VVYXk5GT8z//8D6ZPny5xxHdmWXSo1Wr069cPYWFhYBjGqnf2L1++jMrKSocaXiWlpqYmFBUVYfLkyTY7jG0ymcTWt/X19XYdztVTgiCguLgYgwYNovatv7jVGYPOnY8GDBgglpXZMrm3hb///e/ipHtrlUsdPXoUGzZsQF5eHgDgtddeAwCsXbtWvGbu3LnYsGEDpk+fDqPRiLCwMOh0Ovq+I87mlt+w9FeWEDvq168foqOjER0djQ0bNuDs2bNQqVR44IEHEBwcjDlz5uCTTz7B6tWrnSIxAIAhQ4YgIiICERERaGtrg1qtxo8//giz2SyWHvX2bICl40xjYyPi4+NdrhyiNxoaGnD8+HGbH8b29PREWFgYwsLCOrS+PX36NPz9/cXWt1K/JmazGcXFxfD29nbIXTYp3O7wcb9+/eDr6wtfX1+MHz9eTO6PHz/uVOdP/vGPfyArKwsZGRlWPUdRUVGB4cOHi/8PDw9Hfn7+La/p378//Pz8UF1dbbUdPEKkRskBIRKKiorCiy++iBdffBH79+/H448/joiICOzcuROCICAtLQ3BwcFSh9ltgwYNwujRozF69Gixlv3kyZMwGAziouNWpVSdCYKA06dPw2QyIS4ujhZ9AGpra3HixAnExcV1++toDR4eHggODkZwcLDY0YrneZw9exY+Pj7iLAV77+qYzWYcP35cLL8jPe9KdGNyb/mZPX36NNra2m7Z+UhqX331FbZv345du3ZZfbejq2qKzp97d64hxJlRckAc3s6dO8W77AUFBYiLi+vyujsdInNkRUVFeO655/DNN99g8uTJKCsrQ0ZGBhYtWgQvLy8olUqkp6dDLpdLHWq3DRw4ECNHjsTIkSOh1+uh0Whw5swZtLa2iqVHPj4+Xf5RtdwNHjx4MKKjo+kPL4Dq6mqcOnUKCQkJ3T7Ubgv9+vWDTCaDTCbr0NHq4sWLGDx4sFjLbutzISaTCUVFRQgMDMTYsWNt+lzOoq/tSm/8mbV0Prp06VKHzkcymUzSsrKtW7fiyy+/xO7du23SlCA8PBzXr18X/19eXn5TFzDLNeHh4TAajaivr6dZK8Sl0JkD4vDOnj0LDw8PrFixAm+99VaXyUF3DpE5qm+//RZr164Fx3EYPXr0Te8vLy9HRkYGMjMzIQgC0tPTsWjRog5b387EYDCgsrISarUazc3NCAkJgVwuh7+/P/r16ycu+mQyGcaNGyd1uA7Bsuhz9C5Nllp2jUYjTvG1RS27yWRCYWEhQkJCMGbMGKs+trOy5RwDS+cjtVqNmpoaycrKdu7ciQ8++AA5OTk2K3syGo2IjIzEgQMHMGzYMCgUCnz99deYOHGieM0HH3yAU6dOiQeSMzIysGPHDpvEQ4gN0YFk4vxmzZp1y+SgO4fIHFFlZSUefvhh7Ny5s1vlQxqNBpmZmVCpVGhra0N6ejqUSqXTttHr3Jc9MDAQNTU1GDVqlNN+TtamVqtx8eJFJCQkOFWP+hun+AqCIJaV9XU2hWUStFwup++RX9hzwNmNgxJ1Oh2GDh0qlpXZsvPRrl278M477yAnJwe+vr42ex4AyM3NxapVq2AymbBs2TKsW7cO69evR1xcHBYuXIi2tjY89thjKC4uhkwmw7Zt2yhJJc6IkgPi/G6XHHAch7179+Kzzz4DAGzZsgX5+fnYtGmTvcPsMbPZ3Kttep1Oh6ysLHAch/r6eqSmpkKpVDrt3fbW1lb88MMPGDRoEPR6PQIDA8EwDAIDA922rKi8vBxlZWVISEhw6paTllp2nueh1+s7nD/pyWtrNBpRUFCA8PDwW06CdjdSTj7uqvORpazMmrtFOTk5eO2117Bnzx74+/tb7XEJcXPUrYg4tjlz5kCj0dz09o0bNyI1NfWOH+/MB8R6W78bHByM5cuXY/ny5aipqUF2djZWr14NrVaLBQsWgGVZREVFWTla27D07J80aRJCQkLEMoaKigqcOnUKAQEBYBgGQUFBDtdG01bKysrA8zzuvvtup2/femMtu6Ws7Ny5c2hpabmprOxWDAYDCgoKMHLkSISHh9sxesclZWIA2KfzUV5eHjZu3EiJASF25Nx/cYjL2L9/f58+vjuHyFyZTCbDE088gSeeeAL19fXIycnBCy+8gOvXryM5ORksyzrswd7GxkYUFRUhJiZGPNTn4eGBkJAQhISEQBAEsY1mSUkJ/Pz8wDCMQ7TRtJVLly6hqqoKCQkJLvc5DhgwAOHh4eJhTp1Oh8uXL3c49Np5t8hgMCA/Px+jR4/GsGHDJIzecUidGHTlVp2P2tvbxSSwJ52PDhw4gPXr12PPnj104JcQO6KyIuI0bldW1J1DZO6oqakJubm54DgOpaWlmDdvHliWxZQpUxwiUbC05pw2bVq36ohvrHfWarXw8fEBwzAICQlx+rvrwM+f34ULF9DY2IipU6e6zS4JcPOh14CAAHExWVhYiLFjxzpVty5bcsTE4HYsk7fVajUaGxtvmQTe6NChQ3juueewZ88ehISE2DliQtwCnTkgziszMxMrV66ETqeDv78/YmNjkZeXB57nsXz5cuTm5gLo+hAZ+Y+Wlhbs3bsXHMfhzJkzSEpKAsuyiI+PlyRR0Ol0KCkpgUKh6NUhVUEQUF9fD57nodVqMWTIEDAMY/ODkbYiCALOnDkDvV6P2NhYh0jepCIIAmpqanD9+nWUl5cjICAAo0ePdpkksC+cLTHozGw2Q6fTQaPRiJ2PWltbERMTI/4eOHz4MFatWoWcnByEhYVJHDEhLouSA0LIf7S1tWHfvn3gOA4nTpzA/fffD6VSicTERLvcrbZ04ImPj7fKwUXLwUie51FZWYmBAweCYRi79Nu3BkEQcPLkSXh4eDhs+Ze9tbW1IT8/HxMmTMDAgQM7JIGWQ6/OmAT2hbMnBp1ZdgL/9re/YefOnRg5ciSmT5+OnJwc7Nmzh0rICLEtSg4IIV3T6/X47rvvwHEcCgoKMHPmTLAsixkzZtik3v3atWu4du2aTTvwNDU1ged5aDQasYOKXC53yAWVZeDbkCFDMGHCBEoM8HPnqvz8fEycOPGmFr83JoG26o7jiFwtMejMbDbj66+/xptvvglPT0+EhoYiPT0dqamptHtAiG1QckAIuTODwYBDhw5BpVLhyJEjSExMhFKpxKxZs6yykL906RJ0Oh3i4uLsVh7S0tICnuehVqvh4eEhJgqOMEzMbDajqKgI/v7+iIyMlDoch2BJDCZNmoTAwMDbXmvpjqNWqwFAfG2lnCBtC66eGABAcXExli1bhszMTIwaNQpXrlzBrl27kJWVBbPZjIULF2Lp0qV0/oAQ66HkgBDSMyaTCYcPHwbHcTh06BAUCgWUSiXmzJnT41IdQRBw7tw5NDc3S3rQtrW1VVxMms1myOVyMAwjyWLSaDSiqKiIpvzewNLSdvLkyT3uTtPW1ibOUjAajR1mKTgzd0gMTp48iaVLl0KlUiEiIuKm92u1WuzevRv3339/l1PkCSG9QskBIaT3zGYzjh07Bo7jcODAAcTExIBlWTzwwAN3LOew1NMDwOTJkx2mbKa9vV1MFAwGA8LCwsAwTJ96sneXpWf/8OHDaZjXL5qamlBUVITY2Ng+97PX6/WorKwEz/NobW1FaGhoj9toOgJ3SAzOnDmDJUuWYMeOHbR7Roh9UXJACLEOQRBQWFgIlUqFvLw8REVFgWVZPPjggzfdgW9vb8dXX32Fe+65x6Hr6fV6vXjXub29HaGhoWAYpscTfLv7XPn5+RgzZgwduPyFZdbF1KlT4efnZ9XHNhqNYhvNhoYGBAcHQy6XQyaTOez3I+AeicH58+fx8MMPY9u2bZgwYYLU4RDibig5IIRYnyAIOHHiBDiOwzfffIOIiAiwLIv58+dDEAQ8+OCDuO+++/DXv/5V6lC7zTLBl+d5cYIvwzBWuets6cAzfvx4OmT5i4aGBhw/frzbsy76wmQyibMUamtrIZPJIJfLHW7ytjskBqWlpWBZFv/85z8RHR0tdTg2d+rUKTz55JM4cuQIAODHH3/Ec889h++++07iyIgbo+SAEGJbgiCgpKQEHMdh165dqK+vx7x58/D6669b/W6wvVjuOvM8j8bGRnHKa0BAQI8Thdt14HFX9fX1+PHHHxEXF2f3swFmsxk1NTXgeR7V1dXw8/ODXC5HSEiIpFOp3SExuHLlCtLT0/Hll18iJiZG6nDswmw2g2EYVFRUwNPTE/fddx/efvttTJ06VerQiPui5IAQqdXU1ODhhx9GWVkZRo0ahR07diAgIOCm6zw9PTFp0iQAwIgRI5CdnW3vUPuksrISaWlpWLJkCRoaGpCdnY2goCCwLIvU1NQeHzR1FCaTCTqdDjzPo76+HoGBgWAY5rZTXi2am5tRWFjYq4O2rqqurg4nTpxAXFycXc553I4gCKirqwPP89DpdBg6dCjkcrndB+q5Q2Jw9epVpKWl4fPPP3e7hfHs2bPx7rvv4uLFi8jOzsaXX34pdUjEvVFyQIjU/vSnP0Emk2HNmjV4/fXXUVtbizfeeOOm67y9vdHU1CRBhH1XVlYGpVKJN998E7NnzxbfXlpaCpVKhaysLPj4+IBlWaSlpTntHXSz2YyqqirwPH/H8hRL2Ywt6umdVU1NDU6ePNnr6di2ZBmop1arodFoMHDgQHGWgi0X7O6QGJSXl2PhwoX4+OOPER8fL3U4drdu3TqEh4fjww8/xN69e+nMEZEaJQeESG38+PE4ePAg5HI51Go1Zs2ahfPnz990nbMmB5auI59++ikUCsUtrysrK0NGRgYyMzPh5eUFpVKJ9PR0yOVyO0ZrPZ3LU/z9/SGXyxEcHIzGxkYUFxdLUjbjqKqrq3Hq1CnEx8c7xTyC5uZmsauVreZkuENiwPM8UlJS8P777yMxMVHqcCSxe/duPPHEE3j66afxl7/8RepwCKHkgBCp+fv7o66uTvx/QEAAamtrb7quf//+iI2NRf/+/bFmzRqkpaXZM8xe27t3L0aMGIG77rqr2x9TXl4uJgqCICA9PR2LFi3C8OHDbRip7QiCgNraWnHomsFgQFRUFIYPH263oW+OrKqqCqdPn0ZCQoJDDKHrqdbWVmg0GqjVaphMJnGWQl/KotwhMaisrERycjLeffddzJgxQ+pwJHPx4kXce++9uHjxosPtmBG3RMkBIfYwZ84caDSam96+ceNGPP74491KDnieB8MwuHz5Mu6//34cOHCgy8FArkaj0SAzMxMZGRlobW1Feno6lEolRo0aJXVoPabValFSUoKoqCjU1NRAq9VKVsfuKCyL4ISEhDvOxnAGlva3arUabW1t4iwFX1/fbh9Wd4fEQKfTITk5GW+88Qbuu+8+qcOR1DPPPAOFQoHHH39c6lAIASg5IER63S0rutETTzyBBQsWgGVZO0XpGHQ6HbKyssBxHOrr65GamgqlUolx48ZJHdodaTQaXLhwAQkJCeKCz1LHzvM8KisrMWjQILGOvafTpp1RZWUlzp8/3+Fr4koMBoM4S6G7Xa3cITGorq5GcnIyXn31VSQlJUkdjmQuXbqE5ORk/OpXv8Lnn38udTiEWFByQIjUnn/+eQQGBooHkmtqavDmm292uKa2thZDhgzBwIEDUVVVhenTpyMrK6tHpTqupqamBtnZ2VCpVNBqtWKyFBUVJXVoNykvL0dZWRni4+Nvu+i/8cDrgAEDwDCMzQ+8SkWtVqO0tBQJCQlukQhZulqp1WrU1dUhMDAQcrkcgYGB4mF1d0gMamtrkZycjJdeegkPPvig1OEQQm5GyQEhUquursavf/1rXLt2DSNGjMDOnTshk8lQVFSEjz/+GJ999hl++OEHrFixAh4eHjCbzVi1ahV++9vfSh26w6ivr0dOTg44jsP169eRnJwMlmURHR0t+bTbq1evoqKiAvHx8T06X9D5wCvDMJDL5S5RelNRUYErV64gISHBLUupzGYzqquroVarxcPqQ4YMgVqtxvTp0102Maivr0dycjL+/Oc/IyUlRepwCCFdo+SAEOJampqakJubC47jUFpainnz5oFlWUyZMsXuicKlS5eg0+mgUCj6NECrtbUVPM9Do9FAEASxM44zdPXprLy8HFevXkV8fLxbJgadCYKAy5cv4+LFi/Dy8oKvr684dM2Vvj6NjY1YsGABnn32WSxatMjqj+8u82IIsQNKDgghrqulpQV5eXngOA4lJSVISkoCy7KIj4+3aaIgCAIuXLiAhoYGTJs27aYZB33R1tYm7ihYqzOOvVy7dg3l5eU93kVxZTeWEnl5eaGhoQFqtdqlzqA0NzdjwYIFePLJJ/Hwww/b5DncYV4MIXZCyQEhxD20tbVh37594DgOJ06cwP333w+lUonExESrLt4FQcCZM2fQ3t5u890KvV4vJgrt7e1iouDr62uz5+ytsrIyqNVqKBQKSgx+caczBk1NTeIZFE9PTzFRcKZ2ry0tLVi4cCH+67/+C48++qjNnsfV58UQYkeUHBBC3I9er8d3330HjuNQUFCAmTNngmVZzJgxo0/lP4Ig4NSpUwCASZMm2bWMyWAwiC00W1paEBoaCoZhetRC01YuX74MrVbb5/IqV9LTw8etra1iImg2m8XSMkfui9/W1oa0tDQsXrwYTzzxhE2fy9XnxRBiR5QcEELcm9FoxKFDh8BxHI4cOYLExEQolUrMmjWrRzXfZrMZJ06cwKBBgxAVFSXpgtxoNKKysrJHLTRt5dKlS6iqqoJCobDqDo0z62tXovb2djERvHHHyMfHR/JE0KK9vR2LFi1Ceno6li9fbpXHpHkxhNgFJQeEEGJhMplw+PBhcByHQ4cOQaFQQKlUYs6cObet+TabzTh+/Dj8/PwQGRlpx4jvzGQyQavVgud5NDQ0ICgoCAzDQCaT2XwheeHCBdTX11v93IUzs3a7UoPBICaCzc3NYiLo7+8vWaKg1+vx0EMPYd68eXjqqafs8pw0L4YQq6HkgBBCumI2m3Hs2DFwHIcDBw4gJiYGLMvigQce6NBOtKmpCStXrsTatWsdLjHozGw2i732a2pqEBgYCIZhOvTatwbLgeympiZMmTKFEoNfaLVanDt3zmZD3yyJoFqtRn19PYKCgsRZCvZKFAwGAxYvXox7770Xf/jDH+zynADNiyHEiig5IISQOxEEAYWFhVCpVMjLy0NUVBRYlsXdd9+NtLQ0/PrXv8bzzz8vdZg9Yum1z/M8ampq4O/vD4ZhEBwc3KfFvCAIOHfuHFpbWyVpH+uobJ0YdGY2m1FVVSUmggEBAZDL5QgKCrLZuQ+j0YhHH30U8fHx+OMf/2iT57gVmhdDiNVQckAIIT0hCAJOnDiBLVu24KuvvsLdd9+Nxx57DNxk6EMAABjhSURBVPPnz4ePj4/U4fWKIAioqakBz/OoqqqCr68vGIZBSEhIjxaSlk5NBoMBMTExlBj8wt6JQWeW11etVkOn03WYpWCtzlEmkwmPP/44Jk6ciLVr11rlMQkhkqDkgBDSN3v37sWzzz4Lk8mE5cuXY82aNR3e397ejqVLl+L48eMIDAzE9u3bMWrUKGmCtRKtVouFCxfihRdewJgxY8BxHHJychAeHg6WZZGSkgI/Pz+pw+wVQRBQV1cHnueh1Wrh7e0NhmEQGhp624WkIAg4ffo0BEGwe6cmRyZ1YtCZIAior68XZykMHjxYfH17O0vBbDbjt7/9LUaPHo3169dbOWJCiJ1RckAI6T2TyYTIyEjs27cP4eHhUCgU2Lp1a4ca3g8//BAnT57Exx9/jG3btiEzMxPbt2+XMOq+KS8vR1paGt544w3Mnj27w/vOnTsHlUqF7OxsBAUFgWVZpKamQiaTSRRt3wiCgIaGBvA832EhGRYW1qGTkyAIOHnyJDw9PTFx4kRKDH7haIlBVxobG8VZCv379xdf3xvP1dyO2WzGihUrEBoaildffZVee0KcHyUHhJDeO3r0KDZs2IC8vDwAwGuvvQYAHcoK5s6diw0bNmD69OkwGo0ICwuDTqdzykXE1atXkZaWhg8++ACJiYm3vfbSpUtQqVTIysqCt7c3WJZFWloagoOD7RSt9TU2NoqJwoABA8Q7zmfPnsXAgQMlb+HqSJwhMeispaVFnKUAQJylMGTIkC6vFwQBTz/9NHx8fPD666/Ta0+Ia6DkgBDSexzHYe/evfjss88AAFu2bEF+fj42bdokXhMdHY29e/ciPDwcABAREYH8/HwEBQVJEnNfNDY2oqysDJMmTerRx5WVlSEjIwO7du3CgAEDoFQqkZ6eDrlcbqNIba+5uRkVFRW4dOkS+vfvj4iICDAM0+07zq7MGRODztra2sRZCgaDAUFBQWhtbcW0adMA/JwYrFq1Ch4eHnjnnXcoMSDEddzyh5lm2xNC7qirmwidFwnducZZ+Pj49DgxAIBRo0Zh9erVWL16NcrLy5GZmYklS5ZAEASkp6dj0aJFGD58uA0itp3BgwejoaEBERERGD58OHieR1FREYCf7zgzDIPBgwdLHKX9uUJiAACDBg3CqFGjMGrUKOj1epw9exZ//OMfwfM87rvvPhiNRgwaNAibNm1y2p9nQkjPUFNqQsgdhYeH4/r16+L/y8vLwTDMLa8xGo2or6932hp8awgPD8fKlSvx/fffY9u2bfDy8sKyZctwzz334K233sKVK1ekDvGOzGYzioqK4O/vj8jISAwePBgRERG45557EBcXBw8PDxQXF+P//u//cPHiRTQ3N0sdsl24SmLQmZeXF2JiYnDw4EEUFBSgtbUVP/zwAw4fPow//vGPOHz4MEwmk9RhEkJsjMqKCCF3ZDQaERkZiQMHDmDYsGFQKBT4+uuvMXHiRPGaDz74AKdOnRIPJGdkZGDHjh0SRu2YdDodsrKyoFKpUFdXh9TUVCiVSowbN07q0DowmUwoKipCcHAwxowZc9tr29vbodFowPM89Ho9wsLCwDCM07Z8vR1XTQw627BhA65du4bPPvsMBoMB3333HTIyMpCfn4/ExEQsWrQISUlJtJtAiPOiMweEkL7Jzc3FqlWrYDKZsGzZMqxbtw7r169HXFwcFi5ciLa2Njz22GMoLi6GTCbDtm3b7riodHe1tbXIzs4Gx3HQarVYsGABWJZFVFSUpHGZTCYUFBRALpf3uB2twWAQE4XW1laEhoaCYRj4+vo6/ULSXRKDjRs34vz58/jiiy9umn9hMplw+PBhHDlyBC+88IJEERJCrICSA0IIcWT19fXIycmBSqXCtWvXkJycDJZlER0dbddFtdFoREFBAYYNG4aRI0f2+bEqKyvB8zyam5sRHBwMhmHg7+/vdImCuyQGb775JoqLi/HPf/7TZhOWCSEOgZIDQghxFk1NTcjNzQXHcSgtLcW8efPAsiymTJli00W1wWBAQUEBRowYYfWD0yaTCVqtFjzPo6GhAUFBQWAYBjKZzOETBXdJDN5991388MMP2Lp1q9UmKhNCHBYlB4QQ4oxaWlqQl5cHjuNQUlKCpKQksCyL+Ph4qy6qDQYD8vPzMXr0aAwbNsxqj9sVk8mEqqoq8DyPuro6yGQyMAyDwMBAeHg4Vp8Md0kMPvjgA+zfvx87duzoMPiOEOKyKDkghBBn19bWhn379kGlUqG4uBj3338/lEolEhMT+7So1uv1yM/Px9ixY+0+k8FsNqOqqgpqtRo1NTUICAiAXC5HcHCw5ImCuyQGn3zyCXbv3g2O41z68ySEdEDJASGEuBK9Xo/vvvsOHMehoKAAM2fOBMuymDFjRo9qxdvb25Gfn4/IyEiEhYXZMOI7EwQBNTU14HkeVVVV8PX1BcMwCAkJsXv9u7skBv/4xz+wc+dOZGZm0mA7QtwLJQeEEOKqjEYjDh06BI7jcOTIEUyfPh0sy2LWrFm3LRFpa2tDfn4+oqKiEBISYseI70wQBNTW1kKtVkOr1cLHx0dMFGxdD+8uicGWLVuwZcsWZGVlueUgO0LcHCUHhBDiDkwmE44cOQKO43Dw4EEoFAoolUrMmTMHXl5e4nWXLl3Cq6++ir/97W8IDg6WMOI7EwQB9fX1UKvVqKysxJAhQyCXyxEWFmb1+nh3SQy2bduGTz/9FNnZ2Rg6dKjU4RBC7I+SA0IIcTdmsxnHjh0Dx3E4cOAAYmJiwLIsRo8eDaVSiXfeeQcLFiyQOswea2hogFqthkajwcCBAyGXyyGXyzskP73hLokBx3HYtGkTcnJy4O3tLXU4hBBpUHJACCHuTBAEFBUV4fPPP8f27dsxe/ZsPPLII3jwwQcxZMgQqcPrtaamJqjVaqjVavTv3x8MwyAsLKzH9fOVlZU4f/68yycGWVlZeOutt7Bnzx74+vpKHQ4hRDq3TA4cq2ccIYTYwd69ezF+/HiMHTsWr7/++k3v37x5M4KDgxEbG4vY2Fh89tlnEkRpXf369YNMJsOxY8eQl5eHdevWobi4GDNmzMBDDz2E7du3o7GxUeowe8zb2xvjxo3DzJkzERsbC5PJhKKiIhw5cgSXLl1Ca2vrHR/DXRKDPXv24I033sDu3bspMSCE3BLtHBBC3IrJZEJkZCT27duH8PBwKBQKbN26FXfddZd4zebNm1FUVIRNmzZJGKl1nT9/Hg8//DA2b96M2NhY8e2CIKCkpAQcx2HPnj0YNmwYWJZFSkoK/Pz8JIy4b1pbW8UdBbPZLJYeda6vd5fEIC8vDxs2bMCePXsgk8mkDocQIr1b7hzQCERCiFspKCjA2LFjMWbMGADA4sWLkZWV1SE5cDXnzp3D4sWL8c9//hPR0dEd3tevXz9ER0cjOjoaGzZswLlz56BSqfDAAw8gKCgILMsiNTXV6RaUgwcPxpgxYzBmzBi0t7dDrVbj5MmTMBgMCAsLg1wuR0tLi1skBgcOHMBLL72E3Nxcp3sdCSH2R2VFhBC3UlFRgeHDh4v/Dw8PR0VFxU3XqVQqTJ48GSzL4vr16/YM0eoCAgKwbdu2mxKDrkyYMAHr1q1Dfn4+3nvvPeh0OqSkpGDu3Ln49NNPodPp7BCxdQ0cOBCjRo3C9OnTcffdd2PQoEEoLi5GYWEhZDIZ2tvbcYdddKd16NAhrFmzBjk5OQgKCrLqY+/cuRMTJ06Eh4cHioqKbnndncr4CCGOhZIDQohb6WoR2K9fx93VlJQUlJWV4eTJk5gzZw4ef/xxe4VnE6GhoZgwYUKPPy4iIgJ/+tOfcOTIEfz9739HY2MjlEolZs+ejQ8//BBqtdoG0dqWl5eXuEtw3333wd/fH+fPn8ehQ4dw5swZ1NbWukyicOTIEaxevRrZ2dk2mWMRHR2NjIwMzJw585bXmEwmPP300/jmm29w5swZbN26FWfOnLF6LIQQ66GyIkKIWwkPD++wE1BeXg6GYTpcExgYKP77d7/7Hf785z/bLT5HNWrUKKxevRqrV69GRUUFMjIysGTJEgiCgPT0dCxatKjDjoyj6nzGYOjQoQgPD4fRaIRWq8Xly5fR0NCA4OBgMAyDgICAm5JHZ3Ds2DGsXLkSu3fvhlwut8lzREVF3fEadyzjI8TZ0c4BIcStKBQKXLx4EVeuXIFer8e2bduwcOHCDtfceEc8Ozu7W4sgdzJs2DCsXLkS33//PbZt24aBAwdi2bJluOeee/DWW2/hypUrUofYpdsdPra0QZ02bRpmzpyJoKAglJWV4eDBgzh58iSqqqqcZkehqKgITz31FHbt2oVhw4ZJGkt3y/gIIY6Ddg4IIW6lf//+2LRpE+bOnQuTyYRly5Zh4sSJWL9+PeLi4rBw4UK89957yM7ORv/+/SGTybB582apw3ZYYWFhePLJJ/Hkk09Cp9MhKysLv//971FXV4fU1FQolUqMGzdO6jB71JXI09MTYWFhCAsLg9lsRlVVFSoqKnDy5EnIZDIwDIOgoCB4eDje/bXi4mIsX74cu3btwogRI/r8eHPmzIFGo7np7Rs3bkRqauodP747ZXyEEMdCrUwJIYRYXW1tLbKzs8FxHLRaLRYsWACWZSXZhbFWu1JBEFBdXQ2e51FdXQ0/Pz8wDIPg4GB4enpaMeLeOXXqFB577DGoVCpERETY7XlnzZqFt956C3FxcTe97+jRo9iwYQPy8vIAAK+99hoAYO3atXaLjxDSJZqQTAghRBoNDQ3IyckBx3G4du0akpOToVQqMWnSJJvfRbbVHANBEFBbWwue56HT6eDj4wOGYRASEoL+/e2/KX/mzBksWbIEO3bsQGRkpF2f+3bJgdFoRGRkJA4cOIBhw4ZBoVDg66+/xsSJE+0aIyHkJpQcEEIIkV5TUxNyc3PBcRxKS0sxb948sCyLKVOmWD1RsNeAM0EQUF9fD57nodVqMWTIEDAMg9DQUAwYMMBmz2thGXC3detWu+7MZGZmYuXKldDpdPD390dsbCzy8vLA8zyWL1+O3NxcAEBubi5WrVollvGtW7fObjESQm6JkgNCCCGOpaWlBXl5eeA4DiUlJUhKSgLLsoiPj+9zoiDV5GNBENDY2Aie51FZWYmBAweCYRiEhYXBy8vL6s9XWloKlmW7HHBHCCG3QckBIYQQx9XW1ob9+/eD4zgUFxfj/vvvh1KpRGJiYo8P/kqVGHSlqakJPM9Do9FgwIABkMvlkMvlVonrypUrSE9Px+bNmxEbG2uFaAkhboSSA0IIIc5Br9fju+++g0qlQn5+PmbOnAmWZTFjxow7Hvx1pMSgs+bmZqjVaqjVanh4eIiJwuDBg3v8WNeuXUNqaio+++wzTJs2zQbREkJcHCUHhBBCnI/RaMShQ4fAcRyOHDmC6dOng2VZzJo166Z6/h07dsBsNiM9Pd3hEoPOWltbxUTBbDZDLpeDYRgMGTLkjh9bXl6OhQsX4qOPPkJCQoIdoiWEuCBKDgghhDg3k8mEI0eOgOM4HDx4EAqFAkqlEnPmzIFKpcJf//pX7Nu376aJ146uvb0darUaPM/DaDQiLCwMDMPA29v7pmvVajUWLFiA999/H4mJiRJESwhxEZQcEEJs47777sMLL7yApKQkvPjii2hoaMB7770ndVjExZnNZhw7dgwqlQq7du2C2WzGX/7yFzz00EMYNGiQ1OH1ml6vh0ajAc/z4Hke33//PX7zm99AoVBAp9MhOTkZ77zzDmbOnCl1qIQQ53bL5MDxxjsSQpzKK6+8go0bN+Jf//oXiouL8e6770odkltZtmwZQkJCbtmpRhAE/OEPf8DYsWMxefJk/Pjjj3aO0DY8PDyQmJiIpKQkBAcH45NPPsHp06cxffp0PPLII1CpVGhpaZE6zB7z8vLCiBEjcPfdd2P27NmIjIzEmjVrMH78eMycORPLly/HjBkzpA6TEOLCaOeAENJn9957L5qamnDw4EH4+PhIHY5b+fe//w1vb28sXboUp0+fvun9ubm5eP/995Gbm4v8/Hw8++yzyM/PlyBS69u7dy82bNiAPXv2IDAwEMDPydBPP/0EjuPwzTffYMyYMVAqlUhOTnba782amhosWLAA999/Py5duoSzZ88iKSkJSqUS8fHxPe7mRAghoLIiQoitnDp1CkqlEkFBQfjhhx+kDsctlZWVYcGCBV0mBytWrMCsWbPwyCOPAADGjx+PgwcPQi6X2ztMq+oqMehMEASUlJRApVIhJycHw4YNA8uySElJgZ+fn50j7p26ujrMnz8fL774IubPnw/g57av+/btE9u+zpkzB2+//bbNp00TQlwKlRURQqxPrVbj0UcfRVZWFoYOHYq8vDypQyKdVFRUYPjw4eL/w8PDUVFRIWFE1nH+/PnbJgYA0K9fP0RHR+Pll19GYWEhXn/9dVy9ehVz585FcnIyvvjiC9TU1Ngx6p6pr69HSkoK1qxZIyYGADBo0CCkpKTgyy+/RFFRERYvXkyJASHEaig5IIT0SktLCxYtWoS3334bUVFReOmll7BhwwapwyKddLU77AoLyWefffa2iUFXJkyYgHXr1uHYsWN47733oNPpkJKSgrlz5+LTTz+FTqezUbQ919jYiIULF2LVqlVYuHDhLa/z8vJCfHy8HSMjhLg6KisihBAn545lRdZ09epVsevRgAEDoFQqkZ6eLtnXqLm5GSkpKVixYgUefvhhSWIghLg8KisihBB3tHDhQnz11VcQBAHHjh2Dn58fJQadjBw5EqtXr8a///1vfPXVVzCZTFiyZAlmzZqF//3f/8X169ftFktLSwvS0tKwbNkySgwIIZKgnQNCCHFijzzyCA4ePIiqqiqEhobilVdegcFgAAA8+eSTEAQBzzzzDPbu3YshQ4bgiy++QFxcnMRROweNRoNdu3ZBpVKhra0NqampUCqVGD16tE2er62tDWlpaVi8eDGeeOIJmzwHIYT8groVEUIIIb1VVVWFrKwscByHuro6MVEYN26cVR6/vb0dSqUSqamp+N3vfmeVxySEkNug5IAQQgixhtraWmRnZ4PjOGi1WixYsAAsyyIqKqpXj6fX6/HQQw9h7ty5+P3vf2/laAkhpEuUHBBCCCHW1tDQgJycHHAch2vXriE5ORlKpRKTJk3qVlcog8GARx55BDNmzMCzzz5rh4gJIQQAJQeEEEKIbTU1NeGbb74Bx3G4ePEi5s2bB5ZlMWXKlC4TBaPRiN/85jeIi4vDc889J0HEhBA3RskBIYQQYi8tLS3Iy8sDx3EoKSlBUlISWJZFfHw8+vXrB5PJhMcffxx33XUXXnjhBanDJYS4H0oOCCGEECm0tbVh//794DgOxcXFuO+++1BaWgqFQoGXX35Z6vAIIe6JkgNCCCFEanq9Hrt370ZWVha+/PJLl5hWTQhxSpQcEEIIIYQQQgDQhGRCCCHEde3cuRMTJ06Eh4cHioqKbnndqFGjMGnSJMTGxtIwPEJIlyg5IIQQ4lCWLVuGkJAQREdHd/n+gwcPws/PD7GxsYiNjcVf/vIXO0foeKKjo5GRkYGZM2fe8drvv/8eJ06cuG0SQQhxX/2lDoAQQgi50RNPPIFnnnkGS5cuveU1M2bMQE5Ojh2jcmy9HcBGCCGd0c4BIYQQhzJz5kzIZDKpw3BJ/fr1wwMPPIBp06bhk08+kTocQogDop0DQgghTufo0aOIiYkBwzB46623MHHiRKlDsrk5c+ZAo9Hc9PaNGzciNTW1W49x5MgRMAwDrVaLpKQkTJgwoVulSIQQ90HJASGEEKcydepUXL16Fd7e3sjNzUVaWhouXrwodVg2t3///j4/BsMwAICQkBCkp6ejoKCAkgNCSAdUVkQIIcSp+Pr6wtvbGwAwf/58GAwGVFVVSRyV42tubkZjY6P472+//faWh74JIe6LkgNCCCFORaPRwDKjp6CgAGazGYGBgRJHJa3MzEyEh4fj6NGjSE5Oxty5cwEAPM9j/vz5AIDKykrcc889iImJQXx8PJKTkzFv3jwpwyaEOCAagkYIIcShPPLIIzh48CCqqqoQGhqKV155BQaDAQDw5JNPYtOmTfjoo4/Qv39/DB48GO+88w4SExMljpoQQpwKTUgmhBBCCCGEAKAJyYQQQgghhJA7oeSAEEIIIYQQAoCSA0IIIYQQQsgvKDkghBBCCCGEAKDkgBBCCCGEEPILSg4IIYSQ/9+eHeIADANBEJtK/f+bS5aHNcSmS46ODoBKHAAAACMOAACAShwAAAAjDgAAgEocAAAAIw4AAIBKHAAAACMOAACAShwAAAAjDgAAgEocAAAAIw4AAIBKHAAAACMOAACAShwAAAAjDgAAgEocAAAAIw4AAIBKHAAAACMOAACAShwAAAAjDgAAgEocAAAAIw4AAIBKHAAAACMOAACAShwAAAAjDgAAgEocAAAA8x7255crAACA63wOAACAShwAAAAjDgAAgEocAAAAIw4AAIBKHAAAAPMBQX7390e53UcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1008x1008 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.figure(figsize=(14,14)).gca(projection='3d')\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "ax.plot_surface(xs, ys, zs, alpha=0.2, color='black',\n",
    "                linewidth=1, antialiased=True)\n",
    "ax.scatter(x, y, z, c='k', s=25)\n",
    "\n",
    "for i in range(n_points):\n",
    "    ax.plot(*zip(proj_matrix.dot(data[i]), data[i]), \n",
    "            color='k', lw=1)\n",
    "\n",
    "origin = np.zeros((2, 3))\n",
    "X, Y, Z, U, V, W = zip(*np.hstack((origin, C.T)))\n",
    "ax.quiver(X, Y, Z, U, V, W, color='red')\n",
    "\n",
    "format3D(ax, limits=list(repeat((min_, max_), 3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 2D Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:54.895427Z",
     "start_time": "2018-12-27T18:11:54.769694Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZeThBtUm72ndaud5ubAcws/JwG1SbtKt9ZyzbjczM2qFlQx1J2nqYebs2G1i3aFf7TjdeP2JmjXXi6Bw1E5SkV0laDqyQdLWkKVVPX93uwMquXe07bjcys+F04ugc9UpQXwJeFxGTgfOAa9J7MgGo7ZGVXLvad9xuZFZfJ5YksujE2pV6CWqbiFgKEBE/Bk4EvivpJJJbXVsd7boob7Tr7dYfrzWnjN+XdpQkyrAfOrJ2pda94IEBYPch8/YGFgNrstxPPo/p8MMPD6utv78/enp6Aoienp7o7+/POyQrsDJ+X3p7e4PkJDqA6O3tHfU6y7AfVq5cGf39/dHb2xv9/f2xcuXKvEOqCRiIDMfzmr34JL0WWB0RdwyZvyNwdkR8vi0Zc5SK0ouvqCZOnMiaNWs2Pe7t7WVwcDDHiKzIyvh9aUdP1zLuhyIbdS++iLh2aHJK5z9Z1ORkjXVkNYC1TRm/L+1opy3jfugEvlC3y7iThY1EGb8v7Wj/bfV+GNqmtWTJksK3ceXBF+qamY2xodWQ48eP5+mnn+6aC/BbeaHu87rADDfPzMyyGdolfHBwsOO6iLdCliq+j2acZ2ZmGQxt05o4caLbuIZRbySJ4yT9O7CXpK9WTXOB9WMWoT1PGa7JMLPahrZp3XTTTcyYMYMddtiB8ePHc/vtt/u3TZ02KEmHAH3AZ4BPVj21Brg+Ih5vf3gj1w1tUB4w1qwzdctvO2sbVMNOEpK2joh1LYuszbohQfmaDLPO1C2/7ZZ1kgBeLukaSb+XdL+kP0i6vwUxWpN8TYZZZ/Jve0tZEtQFwFeAo4AjgGnpX8tJGa9NMbPG/NveUpYqvlsiYvoYxTNq3VDFZ2ZWZq2s4rte0pclzZB0WGVqQYxWxT3zzLqHf+/ZZClBXT/M7IiIV7cnpNEpawmqW3rvmJl/7y0rQUXEq4aZWpKcJB0r6R5JyySdM8zzp0taLWlxOr2zFdttp2bPjDrxZmNmNjz/3rPJMtTRbpIukPSL9PFUSe8Y7YYljQO+DhwHTAXeLGnqMIv+KCL60unbo91uuzV7szT33jHrHv69Z5OlDWoucBWwZ/r498D7W7DtlwPLIuL+iHgOuBiY1YL15qrZMyP33uluGzZs6MjrXWx4/r1nkyVB7RoRlwAbASJiPbChBdveC3io6vHydN5QJ0u6U9KPJe0z3IoknSlpQNLA6tWrWxBa85o9M2rXLeKtHC688EImTZrEn/70p7xDsTHg33s2WRLUWkmTSG6fjKQjgSdbsG0NM29oj43/AqZExMHAtcB3h1tRRJwXEdMiYtrkyZNbEFrzfGZkI7Vu3TrOPfdcIoI5c+bkHY5ZYWRJUB8ArgD2k3QT8D3gPS3Y9nKgukS0N7CieoGIeDQi/pI+PB84vAXbbSufGdlIzZ07l6effpoNGzZw0UUXuRRllsrSi28RcDTwCuDdwIERcWcLtn0bsL+kF0naBngTSSLcRNIeVQ9PAO5uwXbNCqNSelq7di2QtFu6FGW1dNv1U1lv+f5y4BDgMJLedm8b7YbTtqyzSTpg3A1cEhFLJX1G0gnpYu+VtFTSHcB7gdNHu12zIqmUnirWrVvnUpTV1Gwv4bLKcqHu94H9gMVs7hwREfHeNsfWlLJeqGvdZ926dey1114M7diz9dZbc9ppp3H++efnFJkVVaeMdt7KoY6mAa+MiL+PiPekUyGTk1mZDC09VbgUZbVk6SXcSdWAWRLUEmD3dgfSDTrpi2OjN2fOHJ599ll6enro6elhq6222vT/c889x5e+9KW8Q7SCydJLuJOqAbOOxdcH3ApUetQRESfUfFGOilzF1+3jb9mWLrvsMu677z4Abr75Zi699FK+/OUvb3r+da97HQcddFBe4VlJlaEasJV31D16uPkR8esmY2urIieoMnxxLB9XXHEFs2bNotHv0ayRMpwIt3Kw2F8DvwN60+nuoianovP4W2bWbp00WECWwWLfSFK9Nxt4I3CLpFPaHVge2t1G1ElfHDMrpk4aLCBLJ4lzgSMi4rSIeBvJNVGfaG9Y+Wh342InfXHMrPMUrSNXlgS1VUT8uerxoxlfVzq+R4uZdbOi9QDMkmh+Kemq9OaBpwNXAj9vb1j5qNdGVLQzCzOzVivaSXqWThL/CHwLOJhkuKPzIuIj7Q4sD/XaiIp2ZmFm1mpFO0nvybjcb0iGOdpIMshrR6q0EQ2naGcWZmatNm/ePGbPns3ixYvp6+sb9iR9/fr1m07S2919PUsvvneS9OI7CTgFuFnS29saVQFl7SLuqkAzK6t6HbnyOEnP0gb1j8ChEXF6RJxGck+mjqziqydrF3FXBZpZJ8rjOs4sCWo5sKbq8Rq2vFV7V8jaRdxVgWZWFkNrfJYsWVKzBiiP6ziztEH9ieTi3MtJbsk+C7hV0gcAIuIrbYyvdPr6+rYYZsSjRZhZUQ1tV3rlK1/J008/PWw7U702+nbJUoK6D/gpSXICuBx4mM1DH1kVjxZhZmUxtMZncHCwUDVADUtQEfHpsQikU+RxlmFm1oyhNT7jx4/fVIIqQg1Qll580yRdJmmRpDsr01gEVzbuwWdmZTK0xuemm24qVA1Qljaoi0h68t1Fch2U1ZDHdQJmZs0arsanSMesLAlqdURc0fZIOoB78JmZtU6WBPUpSd8GfsWWd9T9SduiKin34DMza50sCeoM4K+BrdlcxReAE9QQ9YYJMTOzkcnSzfyQiJiW3g/qjHTquqGOsqjU5957770A7L///u4sYWbWpCwJ6mZJU9seSQfxcEdmZqOXpYrvKOA0SX8gaYMSEBFxcFsjKzF3ljAzG70sCerYtkfRYdxZwsxs9LLcsPBBYCfgDem0UzrPavBwR2ZWJkUdZCDLSBLvI7lY96/S6QeS3tPuwMos68jnZmZFUNR28yydJN4BTI+IT0bEJ4EjgXe1Nywzs8Rjjz3Gxo0exGY0GpWQitpuniVBieR27xUb0nlmZm03ZcoU9ttvP+bNm+dE1aRGJaQ8bkaYRZYE9R2S+0HNkTQHuBm4oBUbl3SspHskLZN0zjDPbyvpR+nzt0ia0orttkJR62zNOs0zzzzDAw88wBlnnOFE1aRGJaSitptn6STxFZLRJB4DHgfOiIh/G+2GJY0Dvg4cB0wF3jzM9VbvAB6PiBcD/wp8cbTbbZWi1tmadaq1a9c6UTWpUQmpqO3mNbuZSzoC2DUifhERi4BF6fwTJG0VEQtHue2XA8si4v50vReT3K33t1XLzALmpP//GPiaJEVEkLOi1tlaOVW+0scff3zOkRRP5XdWsXbtWtauXcvb3/52PvzhDzN37lyOPvronKIrh7IOw1bvOqgvA6cPM/+3wHnAq0e57b2Ah6oeLwem11omItZLehKYBDxSvZCkM4EzAV7wgheMMqxsfK2TtdL06dPZZZdduPLKK/MOpTSeeeYZli9fzu233+4E1UBZb6Rar4pvUkQ8MHRmRCwjSRKjNVxHi6EloyzLEBHnpeMFTps8eXILQmssS52t26ksq913351HH32UiPA0ZKpUTVX09PSw3Xbbccopp/C73/2O97///Tl9atZu9RLU9nWe26EF214O7FP1eG9gRa1lJPUAO5K0heUuS52t26nMWqeSmE4++WSWLFnCxRdfzH777Zd3WKVTphPnegnqWkmfl7RFKUbSp4HrWrDt24D9Jb1I0jbAm4ChN0a8Ajgt/f8U4LoitD9l5XYqs9bYdtttnZhapEwnzvXaoD4IfBtYJqlyZD0EGADeOdoNp21KZwNXAeOACyNiqaTPAAPpXXwvAL4vaRlJyelNo93uWHI7ldnoXXrppRx44IFOSi1SphNnNSqQSNoXODB9uLTS666opk2bFgMDA3mHASRF6aE9Z4rSfdPMutPMmTO3OHGeMWPGmHegkLQwIqY1XK5ENWaZFClBmZkVTRFOnLMmqCy32zAzsw5Rpi7nWYY6MjMzG3P1RpLYpd4LI6IQ3b3NzKwz1StBLSTpsbdwmMmNPEOU6doCM7MyqJmgIuJFEbFv+nfotO9YBlkGZbq2wMwMin9inakXn6Sdgf2B7SrzIqKQrWx59eKbOHEia9as2fS4t7eXwcHBMY/DzCyrvLqcZ+3Fl+WW7+8E5pNcUPvp9O+c0QbYaYp6wy8zs1qKftFull587wOOAB6MiFcBhwKr2xpVCXnwWDMrm6KfWGcZSeK2iDgiHe5oekT8RdLiiCjWO0kV+ULdIlzBbWZWkddFu628UHe5pJ2AnwLXSHqc5486bhkUvThtZt2l6BftZrnl+0kR8UREzAE+QTKA64ntDqwTFb04bWZWJJlGkpB0mKT3AgcDyyPiufaG1ZmytFOZmY1GJ7V1Z2mD+iQwG/hJOutEYF5EfK7NsTWlyG1QZmbtVoa27la2Qb0ZODQink1X/AVgEVDIBGVm1s06qa07SxXfA1RdoAtsC9zXlmi6RKUIPmHCBHbccUd6e3tLXxQ3s2LI0tZdlmrALAnqL8BSSXMlfQdYAjwl6auSvtre8DpTZViktWvXMjg4yFNPPcWNN97IS17yksJ+UcysHLK0dWcZmq0ISSxLG9Rp9Z6PiO+2NKJRKkMb1NBhkar19/cXrr7YzDpLlqHZ2tmW1bI2qKIloLIZ7kK4vr6+TR/8UGWuLzazcqg+BtWqBixCW1bNKj5Jl6R/75J059Bp7EIst+GK0pUi+A477MC4ceM2LTtu3DhfG2VmbZelGrAI123WrOKTtEdEPCzphcM9HxEPtjWyJhWtiq9RUTqvoUbMzOpp57Fp1FV8EfFw+u9WwMNV3cy3B3wEzahRUbroQ42YWXcqwrEpSy++ecDGqscb0nmWwUhHjyhCzxkzK69OOoZk6cX3vJHLJd0REYe0NbImFa2Kb6TKcBW4mRVXGY4hLbthIbBa0glVK54FPDKa4Ky2IvScMbPyGnoMWbRoUWlLVFkS1FnAxyT9UdJDwEeAd7c3rO5VhJ4zZlZeQ48h48aNa3hRblFlud3GfRFxJDAVmBoRr4iIZe0PrTt5xHMzG42hx5CNGzeWtlam4YW6krYFTgamAD2SAIiIz7Q1si5VhJ4zZlZeQ48hQ9ukylQrk6WK73JgFrAeWFs1WYl1Uk8fM6utzLUyWXrxLYmIl41RPKNW9l58Y6UMPX3MrDO1shffbyQd1IKYNpG0i6RrJN2b/t25xnIbJC1OpytaGUOeilB6WbRo0fN6+piZFUmWBHUUsFDSPek4fHe1YCy+c4BfRcT+wK/Sx8N5JiL60umEGsuUTpah7tutegzA4R6bmeUtyx11j2vDdmcBx6T/fxe4gaT7elcowrVOGzdurPvYzCxv9UYzn5j+u6bGNBq7Vcb6S//+VY3ltpM0IOlmSSfWifXMdLmB1atXjzK09ivCtU6HHnroFjEceuihYx6DmVk99UYz/1lEHC/pD0AAqno6ImLfuiuWrgV2H+apc4HvRsROVcs+HhHPa4eStGdErJC0L3Ad8JqIqHu7+TJ0kijCCOZFiMHMulPWThJ1e/Epuehpn4j4Y4uDuwc4Jr2dxx7ADRFxQIPXzAV+FhE/rrdcGRLUUE4WZtZNWtKLL5LsdVnLotrsCqByK/nTSK612oKkndOLhJG0K/BK4LdtiCV3Reg0YWZWNFl68d0s6YgWb/cLwN9Iuhf4m/QxkqZJ+na6zEuBAUl3ANcDX4iIjkxQ7eo0UYTu7GZmzcpyoe5vgQOAB0hGkBBJ4ergtkfXhDJW8bXrollfjGtmRTTqO+pWaUc3c6syb96857VBtUIRurObmTWrZoKStB3JrTZeDNwFXBAR68cqsG7SrgFiG91u3sysyOq1QX0XmEaSnI4D/mVMIrKWKfMgkWZm9ar4pkbEQQCSLgBuHZuQrFV86w4zK7N6Jah1lX9ctWdmZmOtXgnqEEmD6f8Ctk8fV3rxTaz9UjMzs9GpmaAiwsNbm5lZbrJcqGsdwBftmlnZOEF1CQ+nZGZl4wRVcllLRr5o12x47axdcM3F6DhBlVyWktGqVatIBqZPjOSiXf/ArNO1s3bBNRej4wRVcllKRrNnz2bt2rWbHo8fPz7zRbtZE6CTmJVVO2sXXHMxOk5QJZfl7ryLFy9mw4YNmx5HROaYzXeKAAAK4UlEQVT7TWVNgD5LtLJq5x2ui3D37DJzgiq5LMMZjeZHkjUB+iyxmFy6baydQ4J5uLFRioiOmg4//PCwLa1cuTL6+/ujt7c3+vv7Y+XKlS19bX9/f/T09AQQPT090d/f38rwbRT82VgRAQOR4Xje8H5QZVPG+0GVnW9ZX1wTJ05kzZo1mx739vYyODhY5xVm7deSW76bZVEZlHZwcJD58+cXIjm5aivhNhArMyco60juuJFwG4iVmROU5apVJZ2h67n99ttrdtzoptJVEUu3Fc18Dt302RnuJGH5alUj/tD1TJw4seZ63XGgGJr5HFrx2Y2m05C1Bhk7SbgEZblqVRf1oevZsGFDzaotd4svhmY+h1Z8dq2s/nWJrr2coCxXrWrEH7qeww47rGbVljsOFEMzn8NIXlMrebTyBMVtnW2WpZhVpslVfPkbSRVKq6pb8timjU4zn0P1a6ZPnx7Tp0+v+fpa1YGtrOLt7e0NYNPU29vb0vfbqchYxZd7Qmn15ASVP7fx2Fho9D2rlTxamShG8l3372KzrAnKF+pay/niUBsLjb5nM2fOZMGCBaxfv56enh5mzJjB/PnzWxrDSC5S9+9iM1+oa7lxG4+NhUbfs7G4Bmwk3fj9uxg5JyhrOV8camOh0fesaNeA+Xcxck5Q1nKtPjC4K+/YG+k+r7V8Oz+7PBNQM++raAmzFLI0VJVpcieJzuPG5bE30n0+Fj3miqRT39dYwZ0krFO4cXnsjXSf11q+Uz+7Tn1fY6XQnSQkzZa0VNJGSTWDlHSspHskLZN0zljGaMXhxuXWyVo1NdJ9Xmv5Tv3sOvV9FU6WYlarJ+ClwAHADcC0GsuMA+4D9gW2Ae4ApjZat6v4Oo8vcGydrFVTI93ntZbv1M+uU9/XWKEMVXySbgA+FBHPq5OTNAOYExGvSx9/FCAi/qneOl3FZ1abq6asCApdxZfRXsBDVY+Xp/OeR9KZkgYkDaxevXpMgrPycC/AzfKumvJnYSPRtgQl6VpJS4aZZmVdxTDzhi3uRcR5ETEtIqZNnjy5+aCtI3lAz83yvhbHn4WNRE+7VhwRrx3lKpYD+1Q93htYMcp1WocYyRAzvr3GZpVrcfLiz8JGoshVfLcB+0t6kaRtgDcBV+QckxXESM7E867Wss38WdhI5NXN/CRJy4EZwJWSrkrn7ynp5wARsR44G7gKuBu4JCKW5hGvFc9IzsTzrtayzfxZ2Ej4Ql0rpbEYqdrM2qMTevGZ1eQz8bHjnneWF5egzKwul1at1VyCMrOWcM87y4sTlFkD3V7F5Z53lhcnKLMGuv3iUrf3WV7adqGuWafo9iquvC/ute7lEpRZA67iMsuHE5RZA67iMsuHq/jMGnAVl1k+XIIyM7NCcoIyM7NCcoIyM7NCcoIyM7NCcoIyM7NCcoIyM7NCcoIyM7NC6rjbbUhaDTzYotXtCjzSonV1E++35ni/Ncf7rTl57rcXRsTkRgt1XIJqJUkDWe5ZYlvyfmuO91tzvN+aU4b95io+MzMrJCcoMzMrJCeo+s7LO4CS8n5rjvdbc7zfmlP4/eY2KDMzKySXoMzMrJCcoMzMrJCcoBqQ9GVJv5N0p6TLJO2Ud0xlIGm2pKWSNkoqdFfWIpB0rKR7JC2TdE7e8ZSBpAsl/VnSkrxjKRNJ+0i6XtLd6W/0fXnHVIsTVGPXAC+LiIOB3wMfzTmeslgC/C3gO/01IGkc8HXgOGAq8GZJU/ONqhTmAsfmHUQJrQc+GBEvBY4E/l9Rv29OUA1ExNURsT59eDOwd57xlEVE3B0R9+QdR0m8HFgWEfdHxHPAxcCsnGMqvIiYDzyWdxxlExEPR8Si9P81wN3AXvlGNTwnqJF5O/CLvIOwjrMX8FDV4+UU9IBhnUXSFOBQ4JZ8IxleT94BFIGka4Hdh3nq3Ii4PF3mXJKi8UVjGVuRZdlvlomGmefrP6ytJE0ALgXeHxGDecczHCcoICJeW+95SacBxwOvCV84tkmj/WaZLQf2qXq8N7Aip1isC0jamiQ5XRQRP8k7nlpcxdeApGOBjwAnRMTTecdjHek2YH9JL5K0DfAm4IqcY7IOJUnABcDdEfGVvOOpxwmqsa8BvcA1khZL+mbeAZWBpJMkLQdmAFdKuirvmIoq7YRzNnAVSYP1JRGxNN+oik/SD4EFwAGSlkt6R94xlcQrgbcCr06PaYslvT7voIbjoY7MzKyQXIIyM7NCcoIyM7NCcoIyM7NCcoIyM7NCcoIyM7NCcoKyjiBpQ9pddomkeZLG11ju582MSC9pT0k/HkV8D0jadZj5EyR9S9J96cjS8yVNb3Y7RSCpr1a3ZUmT0pG0n5L0tbGOzcrFCco6xTMR0RcRLwOeA86qflKJrSLi9RHxxEhXHhErIuKUVgVb5dskA57uHxEHAqcDz0tkJdMH1Lqu5lngE8CHxi4cKysnKOtENwIvljQlvefNN4BFwD6VkkzVc+enJZerJW0PIOnFkq6VdIekRZL2S5dfkj5/uqTLJf0yvYfTpyoblvRTSQvTdZ5ZL0hJ+wHTgY9HxEaAdETzK9PnP5CWCJdIen86b0p6f7Jvp/MvkvRaSTdJulfSy9Pl5kj6vqTr0vnvSucrvcfZEkl3STo1nX+MpBsk/Thd/0XpiANIOlzSr9P3dZWkPdL5N0j6oqRbJf1eUn86EsZngFPTEu2p1e85ItZGxH+TJCqz+iLCk6fST8BT6d8e4HLg/wJTgI3AkVXLPUBSQplCMvhvXzr/EuDv0v9vAU5K/98OGJ8uvySddzrwMDAJ2J7k3lfT0ud2Sf9W5k+q3u6QmE8ALqvxfg4H7gJ2ACYAS0lGna7EfRDJCeZC4EKSAWdnAT9NXz8HuCONY1eS0dL3BE4mucfZOGA34I/AHsAxwJMk4wBuRTJCw1HA1sBvgMnpek8FLkz/vwH4l/T/1wPXVu2frzX4vBou48mTB4u1TrG9pMXp/zeSjDW2J/BgRNxc4zV/iIjKaxYCUyT1AntFxGUAEfEsQFqYqHZNRDyaPvcTkoP5APBeSSely+wD7A882sT7OYokea2t2kY/yRh9f4iIu9L5S4FfRURIuoskgVVcHhHPAM9Iup7kvlNHAT+MiA3AKkm/Bo4ABoFbI2J5ut7F6bqeAF5GMtQXJInt4aptVAYaXThk22aj5gRlneKZiOirnpEeUNfWec1fqv7fQFLaGO7WF8MZOkZYSDoGeC0wIyKelnQDSQmslqXAIWnb2MYhz9WLozrujVWPN7Llb/p5MY5gvRvSdQlYGhEzGrymsrxZy7gNyqxKJPfFWS7pRABJ29boEfg3knZJ261OBG4CdgQeT5PTX5PcTrvetu4jKXV9uqq9Z39Js4D5wImSxkvaATiJpGQ4ErMkbSdpEkkV3m3pek+VNE7SZGAmcGudddwDTJY0I41va0kHNtjuGpIBls1GxQnK7PneSlJVdydJ+8twN2X8b+D7wGLg0ogYAH4J9KSv+yxQq2qx2jvT9S9Lq+jOB1ZEckvuuSTJ4xbg2xFx+wjfx63AlWkcn42IFcBlwJ0k7VPXAR+OiJW1VhDJLehPAb4o6Y70/b6iwXavB6YO10kCki73wFeA05WMQj51hO/LuoRHMzcbIUmnk3SKODvvWGqRNIek48g/5x2LWbNcgjIzs0JyCcrMzArJJSgzMyskJygzMyskJygzMyskJygzMyskJygzMyuk/wHrTHfZMddc3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_3D_inv = pca.inverse_transform(data_2D)\n",
    "avg_error = np.mean(np.sum(np.square(data_3D_inv-data), axis=1))\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal', \n",
    "     xlabel='Principal Component 1', \n",
    "     ylabel='Principal Component 2', \n",
    "     title='Ellipse in 2D - Loss of Information: {:.2%}'.format(avg_error))\n",
    "\n",
    "ax.scatter(data_2D[:, 0], data_2D[:, 1], color='k', s=15)\n",
    "ax.arrow(0, 0, 0, .5, head_width=0.1, length_includes_head=True, \n",
    "         head_length=0.1, fc='k', ec='k')\n",
    "ax.arrow(0, 0, 1, 0, head_width=0.1, length_includes_head=True, \n",
    "         head_length=0.1, fc='k', ec='k')\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How many Components to represent 64 dimensions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:54.941036Z",
     "start_time": "2018-12-27T18:11:54.896678Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_classes = 10\n",
    "digits = load_digits(n_class=n_classes)\n",
    "X = digits.data\n",
    "y = digits.target\n",
    "n_samples, n_features = X.shape\n",
    "n_samples, n_features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Evaluate the cumulative explained variance "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:55.054849Z",
     "start_time": "2018-12-27T18:11:54.942208Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(n_components=64).fit(X)\n",
    "pd.Series(pca.explained_variance_ratio_).cumsum().plot()\n",
    "plt.annotate('Elbow', xy=(15, .8), xycoords='data', xytext=(20, .65),\n",
    "    textcoords='data', horizontalalignment='center',\n",
    "    arrowprops=dict(color='k', lw=2, arrowstyle=\"->\")\n",
    ")\n",
    "plt.axhline(.95, c='k', lw=1, ls='--');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Automate generation of Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:11:55.062587Z",
     "start_time": "2018-12-27T18:11:55.056365Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(29, 64)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=.95).fit(X)\n",
    "pca.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "512px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
